Being a telepath is hard on her. Its not normal for humans and it nearly drove her mad. ( Thats why her being human is important. Being an alien makes her being a telepath less "difficult") Training on Vulcan saved her life and her sanity. But she is still on edge. Spock being a Vulcan, a "normally" telepathic species, is a threat to her. She feels that he can more readily communicate with Kollos and that Kollos might prefer Spock to her. ( Spock was actually offered the job but turned it down). The episode is built around jealousy. Miranda and Spock. Marvick and Kollos.Then you clearly haven't payed attention to the episode, especially the parts about Miranda's life and background. Also her relationship with Kollos and how that colors her interactions with Spock.
Are these things only possible if she is a human? How so?
She doesn't need to be human to feel jealousy. Most species, other than the Vulcans, show emotions like jealousy. She could be an alien telepath and still be jealous of Spock's ability and better qualifications for the assignment. It would be more believable and consistent for me. She only needs to be human to be a human. She doesn't need it to be telepathic, jealous, insecure or blind.
It certainly is "not normal" for her to be a telepathic human (not at the level she displayed). It is also never encountered, unheard of, unexplained and inessential to the plot.