Well if there is a hiring freeze, she can't give you a job.

. I don't know if you want her to promise it to you if or when it becomes available, with hopes that she'll actually keep her word but with a freeze there's no contract she's gonna have you sign, she ain't gonna put you on payroll so any further communication initiated by you is just wasting your time.
It also sounds like you want some type of win out of this situation. A symbolic victory (which means nothing).
She wasn't really unprofessional, yeah she was late but then again you are at her mercy. She's getting paid, you want to get paid.

she doesn't have to justify her lateness to you, especially if it's internal business matters. Yeah it's one thing if she was sleeping or talking and laughing with coworkers checking Facebook or some frivolous shyt, but lets be honest that likely wasn't the case.
At the end of the day you still need or want a job, whether this event is enough to turn you off from the offer or the company is on you and that isn't a problem, but this internal conflict you have about being right or having been wronged is silly in my opinion.