Good questions! Too bad I can't answer them. :-P

I've also heard that the universe will eventually stop expanding and start contracting. What I'm wondering is WHEN, if it does happen. The sun is supposed to burn out in a couple million years or so. Will the universe contract before or after that happens? If it contracts before the sun burns out, will it contract completely before the sun burns out?

Once we have collected data, how can we be sure our observations about this subject are correct? Earth was thought to be at the center of the solar system (Geocentric Theory) for CENTURIES before Nicolaus Copernicus (what's the correct way to spell his first name?) determined that the Sun is at the center of the solar system (Heliocentric Theory). An interesting thing to note on the side is the fact that the root word of "solar" is 'sol', meaning 'sun'.

Back to the question, time would most likely continue moving forward. There is one problem that I can foresee, however. The human race would most likely be dead by that point (pollution, poverty, famine, drought, etc.), which means this subject shouldn't even matter to us. But it does! Why? Humans hunger for knowledge, simple and clean.

There truly isn't an answer to things like this currently, but in the future it may become clear (you might see it as a reincarnation of your current/past self, if you believe in that concept).