This is a complex question with multiple possible answers. Let's talk about the first question.Some take the simple (and relatively traditional) hypothesis that Europe's location and the blocking of trade links with the east led to their eventual colonial expansion. The rise of the Ottoman empire combined with relative turmoil in central Asia associated with the fall of the Mongol empire helped contribute to spiraling costs for eastern luxury goods. Early exploration was really driven by a desire to cut out the middle men. The position of Europe vis a vis the Atlantic made them particularly well suited to explore and colonize the New World. The Pacific is, after all, a much larger beast to navigate.

Another traditional analysis is that the geopolitical make-up of Europe. This theory basically goes like this: Europe was filled with fiercely competitive states, and that competition helped drive both the technological growth and territorial expansion (Rousseau was a fan of this one).

The last theory I'll mention is sort of a refinement of the last one, which is Diamond's theory as outlined in Guns, Germs, and Steel. This basically posits that Europe enjoyed an insurmountable advantage in terms of resources and human demographics, as well as that competitive edge outlined above. It is touted as some kind of new and innovative theory, but I find it highly derivative of earlier European philosophical/political thought. It is still a good read however (just not one I put a huge amount of stock in).

Which of these are correct? Well, if you asked me for my personal opinion, it would be all of them (and there are even more that I won't get into). Each of them covers an aspect that helps explain how things came to be, but each alone is far from satisfactory. Some of them explain the capabilities, but are shy on rationale of human actions (such as Diamond's work) while others do the opposite.

To your second question, the answer is: of course. I think China is probably the best example. Modern day China exists because of colonialism, and indeed, China's history in terms of progressive expansion outward is not that different from the United States'. The dominant Han Chinese cultural group did not simply arise organically over the whole area. They have been progressively expanding for two millennia, displacing native groups as they did so.