What terminologies are used when ATC instructs a pilot to stop or proceed with his transmission?
If a pilot forgets to release his mic button, you can't talk to him. VHF radio is simplex, so only one station can transmit at the time. If more than one station transmits at the same time, the signal will sound garbled. As a result, there is no standard phraseology to use in such a situation. All you can do is wait for the pilot to discover the issue. See this question for additional info.

CPDLC (text based communication between ATC and the cockpit) does have a "CHECK STUCK MIC" message that can be sent to aircraft on a frequency with a stuck mic. But CPDLC is not globally available, and only used in the en-route environment.

When someone is waiting to transmit, ATC will use the phrase "Go ahead" to indicate that they can start their call. This will not be very useful in the case of a stuck mic, for the reason described above, but the "Go ahead" phrase is often used in other cases where ATC has told a pilot to wait ("Standby"), typically because ATC is busy on the phone or another, more important radio call has to be made first.