Pumping down to see how fast the water flows at 10 gpm or more draw (better test during the dry season) would be useful to check that you have enough water. You probably have enough water.
After testing, I would sanitize the well and plumbing, dump the chlorine, draw water, and then test for coliform bacteria and other stuff. If the water stays clear of coliform when testing, I would be eliminating the UV myself. UV won't hurt, but may be unnecessary.
You would probably want to improve that cover.
I am also thinking that a better seal where the pipes go through the wall of the well would be good to keep surface water from coming in there.
I am not a pro.