First off - with questions like these you might want to check into the newbies section. However - to "answer" your question. Technically, yes, you can record drums with one computer mic but it isnt going to sound that great. This is like saying can FOX show a football game on TV using one camera - yeah but its not going to be that exciting.
As far as your second question - it sorta depends what vocal mics you are using and what you actually are intending to do. Basically - once again - you are not going to get the best sound because you are micing with the wrong tool (most likely). However, if you have 4 vocal mics (for instance) - put each one onto its own channel, set the levels, and while listening thru headphones adjust the mix (this is if you are just dumping it down to a mix instantaneously). As far as placement - try one on the snare, 2 overheads and one on the kick. Your kick will most likely sound like crap if you are using some radio shack vocal mic but you can try it out.