Yes, you bake the plaster with the clay in a normal cooking oven. The plaster does not catch fire at this low temperature, but should be supervised and not left alone while in the oven. Though the plaster will get brown after a few bakings and should be replaced.
Yes, it should be alright, i had no problems with it. You should just open the windows while and after baking, cause the foam smells a little bit. If you are not sure about that, use some aluminum foil instead of foam. But always cover your base completely with plaster. Don't leave a gap! Foam (especially styro-foam) expands in heat and can crack your base and your sculpey work, if not completely covered!