Can a scratched record...

Not that I’m aware of. In fact, I've owned CD's that in spite of careful and repeated cleaning, would not stop skipping.

Sometimes the software is just damaged. Enjoy as it is or dispose of it for a fresh copy.

There is a machine that is $400.00 that heats up a record and allows any warps to go away. Beyond that I do not know. Good Luck.

A scratch that traverses several grooves is impractical to repair (although digital copy and offline software can do wonders for recordings of historic value). However, a simple "dig" that affects only a couple of grooves but causes the record to skip, or worse, repeat, can be fixed by delicate surgery with a sewing needle. Of course the defect will remain audible, but at least the LP is playable.

No first hand knowledge, but I understand that you can play a record "wet" and at least reduce the audible effects of the record damage. Can anyone explain or comment?

Playing a LP wet was common among audiophiles 50 years ago. It was a trick we picked up from radio stations, and has the effect of reducing surface noise. It probably also limits HF signal, which was not a problem for AM radio. Its effect is for steady-state noise, and it won't do anything for a scatch.