In short, they are all grammatically correct.
(1) He proposed to her, who had requited his love from the moment they met.
(2) She, whom he had met only two weeks before, thought his proposal premature.
(3) I am asking her, who is a doctor.
These are all examples of a non-restrictive relative clause, and the relative pronoun takes the case needed in the relative clause, completely independent of the referent, whose case is determined by the main clause. So "who is a doctor" is correct, and the case of "her" is irrelevant. The same goes for possessive and other cases:
He was talking to her, whose family had recently moved in next door. [from "his family"]
A year later I again met him, to whom the kingdom now belonged. [from "belonged to him"]
You should be careful of him, about whom there are many strange accounts.
We ought not to praise them, because of whom many people have suffered. [from "suffered because of them"]
But as John Lawler said, (1),(3) are rather unusual, because they have a pronoun as an object of the main verb and as a referent of a non-restrictive relative clause. Here are smoother alternatives, but they have possibly with slightly different meanings from what you may have intended:
(1) He proposed to her, the very one who had requited his love from the moment they met.
(3) I am asking her, since she is a doctor.
As for the last one:
(4) It is he whom they provoke to anger.
"whom they provoke ..." is neither a restrictive nor non-restrictive relative clause, but still a subordinate clause and hence follows the same case rules as for relative clauses. However, the "it" here is part of a fixed construction, a type of cleft sentence, and does not change even for the plural:
It is they who want this.
It is they whose advice we sought.