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Is it possible that a female painted and a male RES mate?

Sure. There are all kinds of hybrids runnin around out there. I've seen res/maps and res/cooters.

wow, so what do ya think they look like?

Here's a list of hybrids from ATP

http://www.austinsturtlepage.com/world_of_turtles/index-5.html

wow thats awesome. I just got an eastern painted yesterday and put her in with my male RES. The RES is always trying to check her out but she sometime snaps at him but they'll be okay i guess.

A quaratine period of 90 days is recommended before introducing a new turt to one you already have.

For those 90 days, would you need adaquite filtering, heating, and lighting??

Yes, the quarantine tank/container would need to be a complete setup as not to hurt the new turtles health. It's necessary to do this to insure the health of both turtles. Sometimes it takes a while for symptoms of illness to present itself in turtles.

What if the turtles were together when I bought them? And have a clean bill of health from the vet?

That's fine in that occasion. But if you have one healthy turtle and want to introduce a new one into his habitat, it's the safest thing to use the 90 day quarantine system.