When a golf tournament has only three rounds, Is the cut after 1.round one...2.after round two...3.no cut involved?

The cut is after two rounds if it's a regularly scheduled 4 round tournament (as most are). If a round is cancelled due to weather or other problems, it's too bad for those who missed the cut. It's not realistic to call a golfer back to the tournament after missing the cut and going home. I presume you are asking about professional tournaments.

Usually after the 2nd round.