My friends I need your advice!!!

I have a client that requires email managment. I am not sure how to calculate time. My client purchased a 5 hour time block from me and now am stumped on how to record time on the emails. So my questions are as follows:

1. My client requires that I check the email 3 times a day. If no emails are rec'd do I calculate a few mintutes for logging on and checking? If emails are rec'd do I calculate time from the minute I log in? For future how should I bill her for email managment?

The clients rate is very very low but I wanted to get my foot in the door with life coaches and there is potential for many referrals. Did I make a mistake by accepting such a low rate client?

Help please