My T offered email early on since he knew I led a pretty isolated life.

We use it for scheduling and talking about therapy issues.

I'm not sure how one would ask for an email when it hasn't been offered. Why do you want it? To talk about difficult things you can't say in person? You could ask to email that info instead, I suppose.

I would definitely ask about the boundaries of contacting your T out of session and what you can expect in terms of any responses. It's much easier to find this out at the beginning than trying to figure it out as you go and get hurt in the process.