Don't know if you've gotten answers to these yet, but here goes:
Only the starting weapon of the girl you use can be upgraded, and only by leveling it to max and then getting a chest.
Pressing the cancel button should skip the chest animations.
The upgrades do add the starting weapons of the other girls to the level-up weapon pool. Not getting one is probably just bad luck, as they don't seem to be any rarer than other weapons. Important to note, though, is the weapons can only be upgraded if you start with the weapon. ...Yes, I know I put this info in twice, but I felt it was important enough to repeat.
As a side note, it seems there's some variance between the girls and what choices appear for level ups. I have yet to see a magnet be available for the demon girl. Could be wrong, though...