The behavior around
bath time sounds normal to me; my Eri (normally a territorial grumpy pants) magically turns into a sweet cuddle bug after baths!
Lots of dragons prefer to drink from the
bath rather than a bowl, too.
Wish I could help with the owie on his lip, you're sure it's an injury or something, not just stuck food?
Is it possible that maybe one of his feeder might have bitten him?
It's really hard to see on the pic, so a close-up shot would be helpful.
If it were outside of his mouth I'd suggest eat applying diluted betadine, but I don't know if that's ok inside the mouth.
Hopefully you get a response soon!!