Bettas can have trouble swimming due to long fins. This is part of why they sleep on the intake of the filter, less work to stay still.
My male flares at his reflection until his tail becomes a bunch of ribbons, it's very common.
I don't understand why they jump, I've never had a jumper, but I assume it has to do with being energetic in a small space.
My roommate says I'll die by giant turtle.