loose door handle (W124)
 

The rear door handles are loose.
They move a little up and down with respect to the door panel.

Because they move, they rubbed the paint and the silvery bare metal is exposed.

Is it an easy job to tighten the door handle?

If done at body shop, how much is it?

Is there a way to prevent moisture penetration due to the loose door handle without tightening (inserting flexible tin rubber?)?

Should I remove door panel to tighten the door handle?

It is not clear to me whether you are talking about the interior or exterior door handle. I would say each can be fixed without the aid of a body shop.

Exterior door handle.
The front part of each handle is loose.

On the side of the door, about two inches from the handle, essentially around the corner from the handle, there is a black plastic plug, maybe 5/8 inch in diameter. Removing that plug will give you access to a screw, allen screw I believe, which should tighten the door handle.