He should have been asked if his ambassador was sending confidential evaluations of the state of UK government
Of course he is. That's part of his job.
Kim Darroch absolutely had to resign, but not because he's sending critical reports of the US government back to Britain (which is his job), but because they have become public. Darroch can no longer work with the US government which is the other part of his job. It's not his fault, it is the fault of whoever leaked a confidential communication. That person must be caught and prosecuted. They have
a) damaged diplomatic relations with an administration known for its capriciousness
b) deprived us of a good ambassador
c) wrecked a man's career
d) made it hard for Darroch's successor - or any ambassador - to send back honest appraisals of bad regimes for fear of those appraisals being leaked and ending their career.
There is nothing good about this affair whatsoever.