Car drop off at Calais Frethun

I expect you can. Have you checked with a car hire company?

My impression of Calais Frethun is that it as a fairly basic station in the middle of fields, and that few trains stop there. Have you looked at dropping off the car in Lille? There are more trains to London from Lille.

Unlikely.

Very few trains from there anymore, and I have never heard of a car hire counter there.

Calais-Fréthun station is 3.3Km from Fréthun, and 9.2Km from Calais Ville station in the centre of the town. It is in the middle of fields with no facilities and only has 3 trains to (or from) London per day.
Double check with the car hire company, but I very much doubt if there is a car hire office at the station.

As Nigel says, unless you actually want to visit Calais, a better option would be to drop the car off and catch the Eurostar at Lille-
If you really want to return the hire car in Calais, you will need to do this in the town and take a long taxi ride to the station.

I've just looked at the Eurostar website and google and their partner, Avis, and also Europcar have facilities about 3 km away from the station.

If they pick up and deliver you, I know not.