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You can try Tweaker's "Terminate PSO2 processes" function, which sometimes works, or just reboot.

There is, yes. Actually it might be on the Memstick, but most Vita game cards "associate" themselves with an account and only clear that when you 'Delete' the application, mainly to prevent trophy...

You'd have to wipe the save on the card (long press, delete, yes to any prompts), then wipe the Vita and log in with another SEN account that you'd bind to your other PSO2 account.

That's not something I've seen ever happen. I've had a Launcher camo sitting in my shop for months on end now, and it's still there. Also a few people on my friends list who have long since stopped...