Does he cycle to work? I don't know if this is acceptable in British English, but in the US we would say the following: Does he ride a bike (or bicycle) to work?
Hi, Do all of them have the same meaning? a) Does he cycling to go to work? Incorrect grammar. You could say eg Does he cycle to work?. b) Does he go to work on a bike? OK, natural. c) Does he go to work by bike? OK, a bit less common.