Does your account have MMR at lvl 25

You can’t be placed in games without an MMR (match-making-rating), so yes, you have one, even on your first competitive game. It’s value is probably 0 +/- 1, in units of standard-deviations.

Presumably a new player can’t group with someone in low bronze, but I’ve never tested.

There is no such quote. Quick play has no effect on competitive. Initial Competitive Skill Rating, Decrypted