I didn't reply to the other poll attempts, but I can see that you really want this info. I only answered two of your questions because the others didn't fit. I go twice a week and email between sessions. For me, the way it works is that I email many days of the week, but not all. Sometimes, a lot, sometimes just a sentence or two. It depends.

My therapist responds to many of my emails, but it's not guaranteed, and I am fine with it if she doesn't. Sometimes she's not available or just chooses not to for whatever reason (same way I am with people who email or call). If it's a big deal and I am really in trouble, then she does email to get me through it. For me, a sign of being in trouble is when there are calls to law enforcement (by me--usually have had an incident due to being triggered) or I have a medical appointment (which often results in a public meltdown).

I like that it's not set in stone that she will reply X number of times or to only certain types of messages. It seems to build more reliability through the unpredictability of it--sort of like the main thing is that the relationship is constant even if the communications are not. I can email as much as I want or need to (so far--it's been a little over 2 and a half years) and she doesn't freak out about that and will reply at some point. I just never know when.

Sometimes I email just for connection, although that's not what I state. It's nothing urgent, so sometimes she replies and sometimes she doesn't.

I like that she doesn't have a formula for this. For me, it has been working.