I have only seen therapists in private practice and use insurance to get some reimbursement from "out of network" benefits. Both of my therapists respond to emails to a limited extent and the second one actually encourages between sessions contact but he only engages in a minimalistic way. No extra charge for any of that.

I personally would find it a bit disturbing to have my emails read by administrative staff, not primarily because they contain top secret things, more because I do not address my communication to them. As for confidentiality, almost anything that goes through the internet can be intruded unless we use specific, extra secure tools for the communication but I doubt any of those are 100% secure either. I personally don't worry about strangers I never see potentially hacking into it, and I think it's quite unlikely that someone would be interested in my stuff to do so, but I can imagine for some people in certain positions this is a realistic threat and something to pay attention to. There are therapists who use encrypted methods and other higher security tools when they are asked for it, but I imagine these would mostly be in private practice.