Welcome to FGRV, Karen, and congratulations on your purchase!
Mold on the belly band caulk is common. I clean it using a scouring paste containing bleach and a toothbrush. It's part of the semi-annual clean-and-wax regimen. It will come back. As far as I've read, there's no issue with toxicity. It's just cosmetic.
By all means, paint
the cabinet doors! It's only a fake printed wood over MDF- nothing special. Some have replaced them with beautiful frame and panel doors. Now if you start talking about hacking up the fiberglass cabinets, that might get some "Scamp purists" riled up… Actually I'm working up the nerve to "hack" a second door in the closet by the door to better access that nice space around the wheel well.
I don't know if painting
the table will work well, though, being a horizontal surface that gets hard use. Many people replace the whole thing with lighter plywood. I'd consider plywood with a laminate surface of my choosing. Trim the edges with plastic T-molding or metal C-channel for a vintage look. There are lots of creative ideas for upgrading the table in old threads.
I'd get rid of the "stinky slinky" tube, and if I were ordering a new Scamp
I'd have them leave it off, as many knowledgable buyers do. A 5" vinyl fence post cover from HD mounted under the trailer is the usual storage solution and allows for a longer hose. There are some old threads with details.
As to the holes left behind, you can put rivets in them with plastic washers and snap caps (but no tube).
PS- To search old threads, your best friend is the "Site Search/Google" option at the bottom of the "Search" menu in the blue task bar under your log-in information.