I am a science fiction fan, and when I watch movies with aliens, I get annoyed at the fact that they're all humanoid. I think, "What are the chances that it will look that similar to humans?" But I wondered recently "What if there is an ideal shape for an organism in a specific environment?" An example is that all mammals have 4 limbs, and all fish have gills and fins (except for some, but I will get to that). What if that is because that is the perfect form for an organism in that kind of environment? Along with that, some fish have evolved to do certain, unique things, whether to camouflage, attack, or develop a symbiotic relationship (am I correct on that?), which brings up the question, how much does the mindset and disposition of an organism affect its end body shape, and how much more random does it make the process of evolution? What I mean to say is, say biologists were able to create organisms and watch them evolve quickly. If you took two single celled organisms that had no similarities, and put them in the exact same environment, would they evolve to look similar? Or would they develop their own, unique ways of surviving in their environment?
All mammals have 4 limbs, and all fish have gills and fins (except for some, but I will get to that). What if that is because that is the perfect form for an organism in that kind of environment?
Different mammals species live in very different environments. We all have four limbs (except exceptions), not because it is adaptive to all of us for a specific environment but because there a strong phylogenetic signal. You should have a look at Why don't mammals have more than 4 limbs?.
All fishes have gills and fins (except exceptions). This is definitely because they inhabit a common environment. Gills allows fishes to get oxygen from water. Fins is a general structure that allows swimming. You will note that marine mammals also have fins (we often talk about convergent evolution) Btw, the post Do fish break a water molecule to absorb oxygen? might be of interest to you
how much does the mindset and disposition of an organism affect its end body shape, and how much more random does it make the process of evolution?
I don't really understand what you mean by "mindset" and "disposition".
Nothing is random except in the consideration of unknowns. One can make sense of a probability only by consideration of a priories. While tossing a coin is often considered as the random event by excellence, a toss of a coin is everything but random if you were to know the exact forces that apply to the coin. So asking is something is random without stating what are the a prioris you consider knowing and not knowing makes no sense (although it may make some sense in quantum physics).
say biologists were able to create organisms and watch them evolve quickly. If you took two single celled organisms that had no similarities, and put them in the exact same environment, would they evolve to look similar?
We are actually able to witness evolution in a matter of weeks in lab with organisms with short generation time such as yeast or E. coli.
The repeatability of evolution is a vast subject. The issue with such question is that it depends a lot. It depends typically on what evolution you are expecting to see and the size of the population. For example a simple change in allele frequency at a selected locus in a large population is typically very much repeatable. But if you think about larger time scale then, most think it is wise to consider that evolution would take a totally different path. There is a famous quote that says:
"If the tape of evolution were replayed a million times, a species like ours would not necessarily evolve" Stephen Jay Gould
You should have a look at Is evolution a predictive theory?.
You are in quite right-track, yes that sometimes happen, which is called "convergent evolution". It is not usually a mere coincidence, there exists a lot of advantages those led the natural selection to occur that way.
Say, fishes and mammals got separate many million years ago. Yet some sort of mammals, such as whales and dolphins got a streamline shape and quite looking like fish. It helps those mammals to swim in water. It is same for penguins, sort of birds expert in swimming in sea.
Probably you've read about homologous organs and analogous organs in school textbooks. Analogous organs (looking or working the same, but different in developmental origin, anatomy, placement etc) are usually the result of convergent evolution. (however convergent evolution could also be seen in homologous organs) Birds and insects... both contains wings. But their wings are completely different in all other aspects except look and function.
In plants also, there are events of analogy. A stem, looking like leaf (phylloclade, found in Muehlenbeckia platyclados, Epiphyllum truncatum , Phyllocactus latifrons). An inflorescence looking like flowers (members of asteraceae), tendrils of different developmental origin. (Leaf tendril of Lathyrus aphaca, Leaflet tendril of pea, Petiole tendril of Clematis sp, leaf apex tendril of Gloriosa superba, Stipular tendril of Smilax, stem tendrix (axial bud) of Passiflora etc.) and millions of such examples are there, which are called 'metamorphosed organs'. From apparent-look they're so similar that to tell their nature is challenging. *
The most accurate similar look is found in case of mimicry, where an organism 'mimics' certain other organism due to 'cheat' certain other third party species, may it be purpose of self-protection (by hiding ownself or displaying a danger-sign) or to disguise from its prey.
snake mimics snake : page source https://en.wikipedia.org/wiki/Mimicry .
Insect mimics leaf, page source https://simple.wikipedia.org/wiki/Leaf_insect
a plant (Arisaema speciosa) inflorescence-spathe mimiks snake's hood. image source: https://commons.wikimedia.org/wiki/File:Arisaema_speciosa_(2944482182).jpg
However, incorrect (or at-least severely disputed) statement in your question, is effect of mindset of organisms. This was told in Lamarckism, which is now almost 100% discarded, and Darwinism is proven, that tells among random inheritable variations, the favorable ones are selected.
However recent study on epigenetics showing that,some molecular tag-marks for activation/inactivation of a gene (arranged from lifestyle and environmental effects), could be inherited sometimes.
Book reference (*):
Botany, for Degree Students/ A.C. Dutta/ 6th Edition/ Oxford University Press.
College Botany/ Vol 1 by Gangulee, Das , Datta/ New Central book Agency
However, though opinion-based, if we took 2 cells from different species (or of even same-species), evolved separately for many million years (for say in same-environment, just genetically isolated), they should give rise to 2 different kingdoms with vast difference in their structure, because evolution is a very-much chance-dependent phenomenon. Yes it is the deficit of our imagination-power to guess 'what if' there were aliens. Due to same cause, the gods and goddesses of various cultures, are highly anthropomorphic, and even having 2-types of sex. Or just like we tend-to describe non-living objects (like a kettle, conical flask or cathode-ray-tube, gear or toothbrush etc) with neck, mouth, teeth, hand, belly, etc.
There could not be any sort of "ideal" evolutionary body, just because of evolution is a chance-dependent process, where infinite thing is possible, not single, "ideal" one. I've read a sci-fi stories that tells about drugs to bring in forward(future) or backward(past) state of evolution. The first-one (future) was made a human being more intelligent. Practically if ever we could invent the first-one, we could never call it evolution-forwarding drug because many thing is possible through evolution. It is possible to get much more stupid future-human also, through retrogressive (regressive) evolution.
Evolution doesn't plan. It's just a selection over the changes that already happened. This is important when you consider any complex adaptation.
But first, let's see a simple adaptation - the "return" of mammals to the sea, as seen with the whales. The split between the proto-whales and their land-based cousins was exactly what led to the new species - some of the population was having benefits from hunting or hiding in the sea, and it meant they were having more food than average, or their offspring survived with a higher chance or such; and among this population, being adapted to life in water was a significant evolutionary pressure. The ones that were better adapted had more food etc., so they were more likely to reproduce, and their offspring more likely to survive, and over time, they got to be bigger and bigger proportion of the whole population. Rather inevitably, they got to look quite a bit like fish - since that indeed is a shape that is exceedingly well suited to life in the sea. This is the mechanism beneath convergent evolution - two different organisms changing to be very similar due to a very similar environment.
But make no mistake - this is not a complex adaptation. All of the changes that happened during the evolution of today's whales required no pre-requisites - a change in bone length here, a more prominent diving reflex there... They didn't get gills. They didn't get an air sac. They're still mammals through-and-through.
A complex adaptation is much more rare, and quickly becomes rather fixed. First, you need an adaptation A, which must be useful on its own (remember, evolution doesn't plan ahead). Then, once the population is almost entirely made of organisms that already have A, it's possible for another beneficial adaptation, B (which depends on A), to exist and build up in the population. As time goes on, and the organisms keep changing, you might get an "updated" version of A, A', which leads to B', and a new adaptation, C, depends on A' and B'... evolution has no tool to make big changes (unless you count humans :P).
Complex adaptations are much less likely to be produced in convergent evolution (since the conditions that favoured A in the first place might not be present in another similar environment, so B will never have a chance of being useful). They also tend to be more fixed - there's a lot less place for tweaking. Consider the eye - while it has been "evolved" independently multiple times, the end results are very different. For example, our eyes have nerves in front of the sensor cells, while octopii have them the other way around. And our approach is worse, of course - it means we have the blind spot where the nerves have to go through the sensory cells, and it decreases the sensitivity of the sensory cells, since there's nerves above them. But it's extremely unlikely that this would ever be fixed naturally - the difference in the evolution happened very early, back when the complex adaptation wasn't there yet. There's no single step that could fix it now (as far as I know), and it isn't advantageous enough to have a chance of propagating in a population even if it did happen through mutation.
This is the second big point. While evolution itself isn't random (it's very statistical), mutation certainly is. Now consider any complex adaptation. You want C, because it gives you an advantage. But C needs B', which needs A', which needs B, which needs A... and each step must have been an advantage of it's own. But what if A is as advantageous as xA, but they are mutually exclusive? And if it so happens that B cannot work with xA? You'll have two populations, one of which is "stuck" on xA, while another is happily Cing. Or, as happened with us and the octopii, xA doesn't work with B, but it does work with xB, which leads to something suspiciously similar to C, yet different.
However, does this really apply to a whole alien biosphere that developed on a planet that is similar to Earth? That's quite impossible to tell. All life on Earth we know of is made of RNA, for example. This doesn't necessarily mean that RNA is the best ever - it may just mean that once RNA appeared, nothing else could survive, or there were complex adaptations that quickly got grafted on top of RNA. DNA is just an "update" on top of RNA - we use it for "main data storage", but it's usually transcribed to RNA before it gets used to build proteins, and signal, and all the other roles RNA has in the body. Every organism on Earth that we know of has a common ancestor - but that doesn't mean that the common ancestor is inevitable, or the best. It may just mean that once life existed, it consumed every other bit of proto-life it found. There's a good chance that new life from scratch simply cannot appear in an environment that's already settled by another form of life.
However, I would hazard a guess that the way aliens most often look in fiction is way too human. There's plenty of things that are 100% "accidental" in the whole ancestry of a modern human. Opposable thumbs sound useful for any tool-making creatures that use a muscle+bone combo; the fact that we have five fingers isn't. The way our heads are shaped is heavily built around the way many individual adaptations shaped our complex adaptations, and is unlikely to be similar elsewhere. A common trope in sci-fi is to have alien species which are humanoid reptiles, or humanoid avians, for example; but why would a humanoid reptile-like female have breasts? Or five fingers? Or hair? Bi-lateral symmetry is almost omni-present in mammals, and it sounds kind of right (it makes many things simpler, it yields well to manipulation and observation in a 3D environment...), but is it really something that would be universal in intelligent aliens?
That said, obviously the aliens in sci-fi (especially movies and TV shows) are designed in such a way to a) make it easier for humans to play aliens, b) make it easier for humans to relate to the aliens, both on-screen and in theatre, c) avoid making silly mistakes in the design of such aliens. Some shows try to handwave this or even outright justify it (the humanoid cats in Red Dwarf had a huge bonus from being as close to human as possible, since they were living on a ship that was designed for humans), with various levels of success (right, Star Trek, seeding life five billion years in the past is totally going to produce similar alien species five billion years later).