In Tohoku, だ can follow verbs and い-adjectives, as I've heard (I've never actually spoken to someone from Tohoku). What purpose does it serve? Is a sentence ending in just a verb ungrammatical in Tohoku? And is this form used by Tohoku women?
That's a misconception. In Tohoku dialect, the copula だ doesn't follow verbs and i-adjective.
It seems some dialect(s) in Kanto or around there has/have that form. But I'm not sure.