Which is correct?

1.They are taking a boat ride on/in the lake.
2.They are swimming on/in the lake.
3.They are playing on/in the court.
4.He is working on/in the farm.  (I have seen versions of both used. In what circumstance it uses “on” and “in”?

I would say the following:

1. on
2. in
3. on
4. on

1.  “in the lake” just as someone might in a regular U-boat
2.  “on the lake” provided no aquatic beginner happens to drown in it
3.  “in the court” if by verb form “play” you mean countless practice balls for symphonic percussion and two catgut rackets to fill out acoustic strings
4.  “in the farm” I suppose only when he’s knee deep in cow manure!

Tripper, have you decided yet if you are on the lake, in the lake, or still pondering ?

Well literally speaking for #1 you’re on the lake and #2 you’re in it.