Why does evolution (namely the evolution of primates into humans) take place both uniformly and universally on the earth? Why aren't there any creatures who have not taken the same evolutionary steps as their same species elsewhere on earth? For example, why aren't there any humans on other parts of the world who look the same as our evolutionary descendants?
It doesn't. Evolution acts on populations, not individuals. I will never evolve, you will never evolve, but humans are evolving, and sure, certain pockets evolve at different rates. Here's a long but straight-forward write up that deals with perhaps the best example, beak size in Darwin's finches. A select population of birds on an island may be evolving rapidly and differently than that same species elsewhere, perhaps eventually resulting in a divergent species. There is no need for natural selection to operate equally everywhere; in fact, the pressures must be different otherwise we would never see the diverse set of species we do observe.
Short answer: it doesn't. All human beings descended from the same group of Homo sapiens. There has been some genetic deviation since, but not enough to call it a "species". Evolution happens, but at very long time scales and not at any sort of defined pace.
Long answer: As the link above shows, evolution is dependent on several key factors. Heritable variation and change to selective pressures.
Think of humans! Different races, especially ones that have not intermixed, are significantly different. indigenous Africans, indigenous Europeans, and indigenous Japanese, for example. All of these races has genetically diverged into distinct populations with different traits, but the isolation between them hasn't been that long. That's why all humans can still reproduce.
Over a very long period of time, Homo sapiens had evolved to become a more advanced, competitively dominant species. although Neanderthals and Homo sapiens did intermix for a while, we're not completely sure how they went extinct. One of the reasons stated is that it's hard for a worse species to exist when a better species comes along.
If I got your question correctly,
you were aware that humans in some way, shape or form have descended from a common ancestor shared with other primates;
You then realized the relative 'distance' of modern Homo Sapiens from these other primates;
You concluded (or know) that there have been various morphological stages in between, none of which has survived until today;
You were basically puzzled by the question why no intermittent evolutionary stages exist of say the human species. Actually, this is not a bad question.
I think it can be explained with population growth. The modern species has just multiplied so dramatically, continuously selecting for certain features, that there was ultimately less and less room for older forms which have not been able to survive into today.
Monkeys also exist today, which means they have 'survived', but their populations are relatively smaller, and in their case, selection has not emphasized too many new features (correct me if I'm totally wrong).
I think especially when selection is fueled by intelligent awareness, its evolutionary momentum increases dramatically. Our older ancestors (early hominid stages) have then simply been outnumbered by the newer ones, dwindled in numbers and simply become extinct whereas the entire monkey-, or for that matter alligator population has selected relatively more traditionally and remained more homogenous (over-simplification!) - so they're still around, too.
On the other hand, today there are in fact many different types of homo sapiens around with somewhat distinct features, but they're all able to reproduce interracially without much of a problem. In the last few hundred thousand years I'd say there was not enough change to reproductively cut off any (isolated?) group from the main gene pool. Just our common, older ancestors were unable to catch up. This could theoretically happen again in the future, maybe not on this interconnected world, but with different human space colonies.
This is another one of those question where the premise is so crazy wrong, it's hard to answer well without writing a thousand words to explain why every sentence is wrong, wrong wrong.
That's ridiculous. Most of the earth doesn't have primates, and 2 million years ago, most of the ones that did exist weren't evolving into humans. The ancestors of today's New World monkeys didn't evolve into humans. The ancestors of today's lemurs didn't evolve into humans.
I don't think this makes any sense as written. We do observe different species sometimes evolving the same response to pretty similar environments, like cacti on different continents evolving in to similar-looking forms, despite being far apart evolutionary. But we don't expect every population to evolve the same way, because evolution builds on the random changes that came before in that population. That's the basic premise of evolution, that's the premise that explains what we see very well, and if you think some other wildly different premise is in effect, and insist on forcing explanations and data to fit something that is just wrong, nothing in biology will make sense to you.