よくないです seems more informal, but doesnt really matter which you use. i wouldnt be going in the pools though lol
depending on where you go, you might pay first anyway
勘定書をお願いします or チェック will probably work
to get attention you can just say すみません and raise your hand
both tokyo and kyoto it depends where you go. there will probably be more foreigners in tokyo. roppongi sucks, it has way too much foreign stuff/people. a lot of the night clubs there are owned by black people and mostly for foreigners. i went there one time and if you didnt have a drink in your hand, a waiter would walk up to you and ask what you want, even if you were on the dance floor. overall though people are friendly and helpful, a lot speak some sort of english. if you are interested in other stuff just ask me.
bowing depends on situation, but you probably dont need to