Versions of After Effects

I don't know what version of after effects works on that system.. can you tell us that?

The biggest difference in the latest version (cs5) is that it's now a 64bit program.. sure there's a new tool or two, but the 64bit nature of it is the most impressive change.

Not a HUGE amount changed from cs2 to cs5.. everything pre cs2 was pretty different though from what I can somewhat recall (that was quite a long while ago)

I can't really speak to the older older versions.. but cs2 onward anyway, AE has 32bit color, which I don't know if final cut does or not. But aside from that without other add ons for After Effects, the color correction tools probably won't be a huge improvement over anything else available in final cut.

As for the rest of your question, what other things would After Effects be used for? Everything other than the initial edit, and the audio edit..
Need an idea of the kind of things you can do with it? Look at http://videocopilot.net/tutorials

If you only want to do Color Correction, get Colorista II: http://www.redgiantsoftware.com/products/all/magic-bullet-colorista-II/
It's one of the best Color Correction Tools out there, it's pretty cheap and even works with FCP, so you won't even have to buy After Effects to do some kickass CCs.

I don't know the version. I updated my friend's Final Cut and she gave me her version of After Effects. It died with my computer. So, I have to get it back. It's probably an early version because she had Final Cut 2 or 3 and was using a G4 with OS 9.

I'm going to wait till I shoot my next project and worry about this. Hopefully it'll be this winter. There isn't much to do on the weekends in Nov - Feb.