The post is way too broad. Many questions are unclear and many questions lack research from your part. But I still wanted to give you some info that may help you. Answers will be short but it would take a whole book to fully answer all questions.
You are often using "They" to refer to some undefined group of people and give a random straw man. Please always backup your claims with a reference. As a consequence most of your questions are opinion-based (which make them off-topic).
Intro course to evolutionary biology
First and before everything else, you should have a look at a short intro course to evolutionary biology such as Understanding Evolution by UC Berkeley for example.
Please do follow some intro course before reading the following. You will get much more from the below answers this way.
You should read about coalescent theory.
- They say humans and monkeys have a mutual ancestor. Was it literally one ancestor? Because if so, then it would need a partner to regenerate children right?
Yes, any two organisms on earth literally have a common ancestor which is a single individual. However, when thinking about closely related species as humans and chimps, the dating of the most recent common ancestor might rather correspond to a population than a single individual. It would be a single individual if there were only asexual reproduction with no genetic recombination.
- Even if they would have children, then these children would be brothers and sisters right, which means they cannot have sex to regenerate their children?
- They say that humans and monkeys have a mutual ancestor, does that mean that a certain brother's family became monkeys and the other brother's family became human?
If reproduction was asexual and if there were no recombination (which at this scale is not too an awful model depending on what predictions you are trying to achieve), yes one individual is ancestor of the human lineage while the other sibling is ancestor of the chimp lineage.
If humans and monkeys have a mutual ancestor, then how come humans and monkeys are so different in terms of intelligence, hygiene, clothing?
They say humans lost our fur because we don't need it anymore, but how come we still need cloths to wear to protect us from cold?
Why do humans have to brush our teeth, cut our nails, use toilets and work for our food and drinks, while any other animals don't?
I will just make one short comment for all 3 questions.
If an oak tree and a pigeon have a common ancestor, then how come they are so different? You could ask the same question with any pair of species. the appreciation of the differences is completely arbitrary.
The terms you use are all very related (all related to intelligence) and fast to acquire. You typically talk about hygiene. Showering / bathing is a very recent human activity. Just a few centuries ago, no one was ever showering (not even the kings) and people were throwing their dejections in the street in cities.
- Why do men and women have those specific features that make a man a man and a woman and woman? Why do women have to give birth and not men?
For these questions, you will need to learn what a sex is, learn about sexual selection and eventually about Bateman's principle. You will note that these questions are not specific to humans.
Why do men have more facial hair growth and are built stronger than woman (while male and female chimpansees (our closest ancestors) both grow facial hair Why do men grow facial hair?)? Some people say men have more facial hair growth and are built stronger because they used to hunt (why did men hunt and not women?), but some say men hunt because they have more facial hair and are built stronger. Wouldn't it be a circle reasoning?
You are imagining a cause-consequence considering only extremes of the two variables. The reality is much more of a smooth process where gender roles happened slowly. Also, there are many factors that affect gender-specific general body size. In most species, females are bigger as females produce bigger gametes and, for the case of mammals typically, carry the baby. Gender roles such as defense, hunting and many other things explain such dimorphism. You will note that there is also similar dimorphism in chimps.
- Why do human male and female look different compared to other animals? Why do human individuals look different from each other, but all other animals look like each other (geometrically)?
The first question could be asked for any species again. For the second question, please have a look at the post Why do different humans look different?.
- Could it be possible that we relate humans to animals, because we associate animal behavior with human behavior due to our human reasoning (which we can't help of course)? But human and animal behavior that look similar, does not mean that they have the same meaning right?
I don't understand the question and it sounds very much a matter of opinion rather than a matter of evidences.
- Does 'survival of the fittest' mean the following?: Humans have finger nails and a protruding nose, because animals that didn't have nails or protruding noses are extinct?
"survival of the fittest" is a typical expression that refers to the process of natural selection. Natural selection is a process that causes a change in allele frequency over time caused by a fitness differential associated with genetic variance. If this decision does not make sense to you, make sure to have a look at an intro course to evolutionary biology.
Why do humans have a chin, curly hair, eyebrows, lips and facial hair above the lips while monkeys don't?
Why do humans have this specific hairline (separation line between hair and skin)
Just one comment for the above two questions.
These questions only are already too broad. You will need to focus on a single trait. You will also need to get some intro knowledge to evolutionary biology as it feels like you would make the mistake of being too adaptionist and misconsidering spandrels.
- Why can human hair and finger nails grow forever, but monkey's hair and nails don't grow that long?
Is this true? You will need a reference for that. I doubt chimps hair really stop growing. They probably just fall as they get long enough. I don't know much about that but I would definitely need some references to really understand in what terms are human hairs different from chimp hairs.
- Some human emotions such as guilt and fear sometimes result in not doing anything at all, but isn't that evolutionary a disadvantage?
Yes, very likely. The field that studies such thing is called evolutionary psychology.
- Humans have so little fur compared to monkeys. Which means that at some point, starting from the ancestor, the next generation lost more and more fur. At some moment there was so little fur left that generation felt cold and wore some clothing? But what about their naked parents who have about the same amount of fur?
I am not sure I understand the question. It feels like you are seeking for a sudden change where everybody suddenly went from being naked to wearing uniforms with bow ties.
- Why are there humans and monkeys, but not intermediate forms that slowly changed from the ancestor to human or ancestor to monkey? Because they would have human characteristics but also monkey characteristic which are still there nowadays?
You should have a look at Where are the evolutionary “inbetweeners”? and Why aren't there any transitional animals today?.
- Could it be possible that new species are not arisen, but just discovered?
Most species that are discovered have not arised any time recently indeed.
- Could it be possible that all the species do not arise in series (after each other), but parallel (at the same time). Because if it would be the former, then the food chain would be incomplete?
I don't understand your relationship with the food chain but yes speciation events occurs in any lineages, not totally independent of each other but in a way that "feels" like something we would call a parallel process and not a serial process.
- Why do we have puberty, and why don't boys already have facial hair when they are kids (for warmth)?
Have a look at an intro course to developmental biology.
- They say humans find a lover because, evolutionary speaking, they want to produce children. But how come some couples choose not to have children?
While evolutionary processes can eventually select for not reproducing (see kin selection), the likely main reason for why many coupled don't want kids have to do with our culture and not with the evolutionary forces.
- Why do humans talk and write (have a language), while monkeys don't?
Because we're intelligent. Many monkeys have some form of primitive communication though with a few words and a few signs.
- They say the big bang was the cause of everything, but how can material appear from nothing?
This is completely unrelated to biology.
(Which basically means 0=1) Even if organic molecules came from an-organic molecules, they it would still not mean that the organic molecules were living? (example: a wooden door is organic, but does not live)
I don't understand your question. But you should have a look at an introduction to abiogenesis
- They say evolution is driven by mutations. Are protruding noses and nails the consequence of mutations? But most mutations are of disadvantages (example: diseases)
The statement "evolution is driven by mutations" is very misleading if not simply wrong. Just have a look at an intro course to evolutionary biology!
In short, evolution is a change of allele frequency over time. There are various processes that can cause such changes. One of which is natural selection (NS). NS is caused by a fitness differential associated with different genotypes. It causes genotypes associated with higher fitness to raise in frequency, therefore removing genotype associated with lower fitnesses from the population.
NS therefore results in a decrease of the within population genetic variance. Mutations brings up new genetic variance in the population. It is true that most mutations are neutral or deleterious and are therefore (by definition of what deleterious mean) counter selected and will eventually disappear from the population. The few beneficial mutations that occurs may eventually increase in frequency through NS and eventually reach fixation (that is a frequency of 1) in the population.