I think it's correct, 1) "Sort of" is an informal phrase that means the same thing as "somewhat." 2) "Somewhat" is an adverb, and adverbs can modify verbs, adjective, and other adverbs. I am sure I can say: "I somewhat dislike broccoli." "I wouldn't have gone to the party, but I somewhat resent that I wasn't even asked." "The sky is somewhat cloudy." "She drove somewhat slowly because the road was slippery." I think I can substitute "sort of" for "somewhat" in each of these sentences. I am not sure about the choice of the word "resent," though. The grammar is correct, but I'm wondering if the person didn't means to say "I somewhat regret that I couldn't go."

The sad thing is that it is INCORRECT to say "I resent that I couldn't go"! "Resent" must take an object, and you must write "I resent the fact that I couldn't go." Regarding "sort of", don't use it. It is a "filler" meaning nothing which is used to fill in hesitation time. It bespeaks of a certain moronic inarticulacy. Perhaps the professor wishes to show that the girl is an inarticulate moron. Either that or (the alternative is too painful to contemplate!)…

Yes, this is used correctly. She feels a little angry that she missed the concert. It's important to know that "sort of" is a phrase and is informal English.

This is a common thing to say "sort of" and then the verb. I try to minimize my use of "sort of." I'd rather say what I mean and mean what I say.

It also has this meaning (I think a bit like نوع) What sort of dog do you have? What sort of car did you buy? He is not the sort of person who would lie to anyone.