There is no reason this program should not work on Windows 7.
The challenges may come if you're using a 64-bit version of the software. Some 64-bit drivers may not be compatible with this 32-bit program.
I have just this week bought the DL version of PrE 8 (after running the trails for a little time). At this point, I have very little experience with PrE (any version), have not installed the purchased version, nor tried to burn to disc with the trial. I have, however, been running Win7 64 bit since it was in beta and am now running Win7U 64 bit RTM.
A few things I would suggest are:
1) Try running in compat mode. You can choose from several modes, including Vista, Vista SP1 & SP2, XP Sp..., etc.
2) If #1 does not help, try running PrE7 as admin.
If none of the above works, you could try uninstalling and reinstalling, but before reinstalling, right click on the setup file and choose a compat mode.
Aside from posting your questions here, you could also post at http://www.sevenforums.com/
As Steve says, with Win7 getting closer to release, things should be pretty well set by now. There were 2-3 builds, about 3 mos. back, that just did not work at all with almost anything Adobe, but later builds seem to have fixed those issues.
Now, with the crashes, this ARTICLE might give you some tips on gathering clues as to what is happening, when the program crashes. Be patient and follow every possible link.