This is going to take time. You are going to have to allow some time for you and your new T to know each other. It's like you want it all to happen right now and perfectly right now when the reality is it will take time and there may be some bumps in the road while you get acquainted.

If you want more than one session a week to get through this initial phase, that is certainly a legitimate request. Yes, she has the option to say that isn't an option, but if you don't ask, you really can't complain. A "no" response would not be a comment on you from what I can tell. It would more likely have to do with her tight schedule.

Don't try to plan ahead. You'll just be disappointed when things do go exactly the way your mind arranged them. One step at a time here.