Usually yeah. You gotta remember that other characters exist and try to come up with a reason, like a Gym Leader retires/Out of Town and uses them as a Backup, or a Champion getting defeated in the Championships, etc.

It all depends on your story and what you want to tell, but just remember about the other canon characters... Because well, they're canon!

Yeah, and that common rationalization is that it's either AU or in a parallel dimension via Ultra Space, so it doesn't conflict with canon - which gives us crumbs concerning certain characters or events. Since there isn't a really solid timeline, I can do whatever I want.