In the official canon(series, movies and authorized books), did Spock and Q ever meet?
Nope. The Q entity is a strictly TNG and onwards character.
Unless you count Trelane, who has similar powers.
Was Trelane’s identity re race/group ever nailed down?
Except Spock was still alive during the TNG timeline, so that doesn’t exclude a meeting of the two.
Q was a mischievous character, and older Spock would probably be too boring for him.
There’s an audio program called ‘Spock vs Q’ on the pocket books imprint (which handles the brand-name star trek books, but are NOT considered official canon.) I thought that it was based off a print book, but can’t find out anything about that. Apparently the audio is read by Nimoy and DeLancie and has some good reviews on Amazon etc.
He only appears on-screen the once, so no, not canonically. But he is identified as a member of the Q continuum in a novel.
Not on screen, but in one novel he’s identified as a member of the Q continuum.