is putting tape around the bottom of the jersey legal, to keep it tight against the body, beacuse they're too short to tuck in?

I couldn't find anything in the rule book that specifically disallows.

Tape on player...
 

I would say yes, a player may tape his jersey. No knot-like protrusions should be allowed though. As long as the tape is applied flat against the uniform and/or body and it does not provide an unfair advantage (sticky surface for catching/recovering the ball, etc.) I don't see any problems.

why is it taped?
 

Shirts should reach the pants and be tucked in.

If you allow tape around the waste you will need tp allow tape around the sleeves, etc..
It could theoretical be a safety issue, should a tacklers finger gets caught in the tape. Don't need the hassle of explaining to some kid's lawyer why you allowed his 9-fingered client to participate in a game where players weren't uniformed properly.

The reason to tape is so that opponents don't have that 'shirt tail' to grab onto when tackling.