Stripping the original paint can be done at home. Jasco brand paint stripper in gel form is reasonably cheap and works extremely well. It's supremely nasty stuff, however, and will burn your skin. And mommy will not appreciate you getting it on her furniture, so outside is probably a good plan.
Carbon fiber frames cannot be powdercoated as the heat is too much for them.
Most powdercoaters who specialize in bicycles will have "holders" made up to fit various portion of the bicycle -- bottom bracket shell, head tube, seat tube, derailleur tab -- so that they can manipulate the frame in the coating booth without touching it.
Powdercoating is normally not completely moistureproof. It is common to strip a powdercoated frame and discover spiderwebs of rust on the steel. Clear powdercoating is available; no, it can't be applied over decals, and it may even be less moistureproof than the colors are.
Probably the best approach is powdercoat with a sprayed-on clearcoat. This both looks better and lasts longer than plain powder.
The "average" price varies, but is probably in the neighborhood of $50, if you do the stripping yourself. Sprayed-on clear adds another $50 or so, in general.
And finally, unless your powdercoater really does specialize in bicycles, there is a very good chance he will miss a few tricky spots like between the seatstays where they attach to the seat lug, and between the chainstays where they attach to the bottom bracket shell. You should also be aware that many powdercoaters will aggressively sandblast a part prior to coating, which can be rough on light-gauge bicycle tubing. Might be a good question to ask of prospective powdercoating shops.