I don't know what a slirp is either, but in the SheepShaver GUI you can select slirp as an option for networking:
http://www.emaculation.com/doku.php/she ... line_guide
Can you try that?
A slightly easier easier way to get online in the emulator. Keep in mind, also, that if you use the IE or Netscape versions that come with Mac OS, they will crash the emulator just like you described. Best stick to using Classilla.
Not sure what to suggest about the My Computer crash. That's new to me. But I guess if you get the networking sorted out it will be less urgent.