Almost all so-called "mystery snails" are apple snails. Apple snails are sexual, either male or female. Females lay eggs above the water line. See
http://www.applesnail.net for everything you could possibly want to know about them!
They will breed in an aquarium but better success is had in ponds. They don't survive below about 50-55 degrees F so they can't stay in a pond in winter where it gets colder than that. If you look on the forum, there are some threads about people who had apple snail eggs and/or babies and what they did.