1. I originally thought 'no' but there was a post on here a while ago confirming that many USB modems do indeed work with Android devices (including the Prime).
2. No. Not in the same way as a PC. As pointed out by several posters in this thread, there are ways of hacking around some things, but Android just isn't designed that way.
3 and 4. That sounds like a faulty device. If I turn off wifi, Bluetooth and GPS, my Prime's battery lasts for days in standby. It almost never crashes or locks up.