The therapist is responsible for clearly communicating ground rules up front. The therapist is being paid to manage the relationship, so you should not have to guess about what is appropriate email communication.

Also, more generally, she should be defining and clarifying the nature of the relationship so you don't have to wonder endlessly, as seemingly most clients do... what exactly IS this. Even though it's nearly impossible to define the therapeutic relationship, since it is so unnatural and so poorly conceived, she ought to try.

As for what is normal re: email, or anything else, good luck nailing that down. I've found they are all just making up the rules as they go, they are accountable to nobody, there is no consistency, and little logical basis for anything. They prefer to keep things as vague as possible, avoid pointed questions, and gaslighting is fundamental to the process. These are generalizations of course, but they are well-founded.