My friend is going to be here this weekend with his 360 and halo 3. Well i was thinking of hooking his xbox 360 up to live, but then i'll have my xbox 360 in either monday or tuesday. Can i still hook mine up later with my own gamer tag?

Does it register by consoles or house?

There is no possibility of registering someone "by house". Once you pay your XBL fee, you pay for your account/gamertag, so you can easily have several XBL accounts in one house, and even on one console.

The GamerTag can be used on any 360. I could post my e-mail address and password and anyone here could use my GamerTag on their 360.

Why they'd want to, I don't know. But, yeah, you can sign up for a tag on his 360 and use it on yours. When you first login with your new 360 hit "Recover tag from XBL" from the menu.