Second:
Yeah, it's called "roaming" and it's more-or-less seamless. Well, okay, it has a small seam, but you don't really need to do much.

Your access points should have the same authentication configured and should be on separate channels. (As a reminder, you should really only use channels 1, 6, and 11.) All modern (and perhaps all always) cards and drivers will handle moving from one AP to the other.

If you're running DHCP, you should probably have it run on a system separate from the APs, or, if that's not possible, run it on only one of the APs and make sure that it responds to both the wired and wireless segments.