Yes, just go to your speaker/audio settins on your PC, I got a gamer's headset but I only use the mic because I have two 12 inch subs set up.
It may be possible. However, you'd have to be a pretty hardcore audio programmer to do so. You'd have to dig around in the game programming to figure out how it assigns voice to channels, and set up some sort of mixer program to assign certain channels to certain outputs. The latter of these can be accomplished with a good software suite for your sound card. The former of these is going to be very, very difficult for someone who has to ask this question. It may not even be possible if Garry's Mod mixes voice across available channels before outputting it.
Unless you're only asking if you can use your headset mic for input, and speakers for all outputs. Then what Snak said.
Oh I think I read what u wrote wrong, you want in-game sounds (like gunfire, explosions etc..) thru your speakers, but you want the player's microphone's to come thru your headset? I don't think thats possible, It's either sound thru your headset or sound thru your speaker, you can't seperate microphone's because that's counted as in-game sound.