1) They do indeed - both intentionally and unintentionally. Katara has caught Zuko doing it more often than he's caught her, but when she's especially happy with him she gives him a show, using her water in some most creative ways. ^^

2) LOL that link. Hahaha, too funny! I think if Katara was Fire Lady and living in the palace with her husband, there would definitely be some exhibitioning going on. ;)