I think it's unprofessional at best. If anyone is dramatic, it's her not you.

From what you said here, she doesn't appear to practice psychoanalytic therapy. For one, consistency in scheduling is a standard in that therapy. I can't help but wonder if she dropped out of psychoanalytic training though many Ts use the label 'psychodynamic' in a very broad sense (i.e, they talk about the past).

The crying and superficial compliments would bother me too. You've only had 5 sessions? Imagine what this will be like down the road!