Conundrums to be spoken of here, so go beserk and expect some spoilers should you unveil the comments.
Update: Here are a few of my queries and conundrums that haven’t been addressed in the comments already:
1 down: Research centre plug plugging 28-across (darling) clothing 11-across (at sea) (3, 6)
3 down: Stalks onstage, it’s said? (7)
4 down: I crack baseball side, well trimmed for online photo (9)
The direct definition seems very wrong indeed to me. Anyone willing to defend it?