I average about once a week, sometimes more sometimes less. Usually I ask him not to reply, to avoid misunderstandings/disappointing responses but sometimes I ask him to confirm receipt and sometimes I ask him for a response.
I've learnt over the years that telling the therapist what you need from them is the best way to reduce the risk of hurt.

ETA - to answer your question your needs are totally normal. It does indicate he's not massively experienced with clients who have out of session contact needs. That's not necessarily a bad thing if he's willing to work with it, but I think it makes it doubly important that you have a discussion together where the boundaries are clearly laid out.