I don't know if this'll help anyone, but I found a way to fix the problem without skipping the scene. I have Windows Vista Home Premium (32-bit) Service Pack 1, and K-Lite Codec Pack installed on my computer. Codec Tweak Tool came with it, and after I disabled AVIsplitter (Gabest), it fixed the two freezes, and finally made the polygon characters function correctly with the FMV's. I also made the game read the movie's from the hard drive, so that might of helped too. I can now go through FF7 without glitches or freezes (as far as I know).
I don't know if having AVIsplitter off all the time is bad, but I haven't seen any problem with it so far. It's easy to turn off and on, so if it needs to be on it's not problem.
I would think this would work for everyone else too. Tell me if it's just my system, or perhaps I just got lucky (I believe I learned about that from the people here).