As for Shabbos issues, Rav Ribiat in his 38 Melochos series goes into detail for several toys and games. He is OK with most puzzles as long as they’re not built in a frame. For something a little more specific, a talmid of Rav Yosef Berger from Baltimore published a kuntrus on his psak halachos of toys on Shabbos and he goes into detail on games and puzzles.
Don’t quote me on this, but I recall one or both paskening that there’s no halachic problem with a game that has play money, it’s just something people don’t do.