1: Yes, the game will recognize it's Japanese.
2: Yes, they will still be shiny.
3: Yeah, trading them between Sun and Moon will work just fine.
4: Yes, you still need to pay, and you pay as soon as you open the software for the first time, before you can access any of the features.
5: There is no way to cancel the subscription, so once you pay the $5, you have a full 365 days to use the software however you please until your subscription ends.
6: As soon as you finish paying, you should get charged to your credit/debit card automatically. And as far as I've seen, I've never got any emails from the software, and I've been using Bank for quite some time.
Source: Experience
If you have any other Bank questions, just let me know!