What time does the play begin?

The second one is correct. "When" has the idea of "what time" already, so it's unnatural/redundant to add the word "time" to "when". You can change the first sentence of yours into "When does the play begin?" though.

What time does the play begin ? It is correct.

either when does the play begin or what time does the play begin will do

what time does the play begin ? or if you want to use "when" you must say : when the play begins ? the first one is more formal