I have never been charged for emails. I don't like phone conversations so I avoid these.
With t #1, I sent emails, and usually she would not commit to any therapeutic words online, just that we would discuss issues at next session.
I only email t #2 once. She did not reply, and at the next session, she just thanked me for information.
Now with t #3, I feel very comfortable emailing, although I have only done this a couple of times. With each email, she has sent thoughtful, detailed replies. Also, she printed these out in order to discuss issues in the next session.
I have not offered to pay, figuring that if she feels she should be compensated, she will tell me so.
Bluemountains