Hi,
1) Personally I use MilkShape to create them, and CharFX to animated them. Pretty different to 2d
so I'd say get some shareware/demo's and give 'em a whirl, see how you get on. If you want to start at the really simple end of things, look for Doga. All of these export to .X...
2) There is a map demo and basic fps demo somewhere, but yes, totally possible. It sounds to me like you'd love TGC's next piece of software, which is an FPS creator. Much easier that writing one from scratch in DBC/DBP, but it depends if you want to program it your self or create it through another piece of software, with less coding. Alternativly, check out Cartography Shop, excellent, and simple to use 3d level editor, good for FPS, exports to .X also.
3) Check out the specs for DBC/DBP on this web site, depends what you need from the software, but IMPO I'd say DB Pro for sure, having owned both for a while now.
Hope it helps,
Cheers.