Great question!
To answer the first few questions, more generally - I bill for time spent on *anything* client-relative and I bill in 15 minute increments regardless of what it is I'm working on.
I also have a client who insists on daily feedback - he's funny because even when I send an emailed 'report' on what we worked on that day he'll ask me the same questions a few hours later (about things I just sent him). I gather that my own client is just really busy, scans my emails rather than actually reading them, and is also just really excited about the projects we're working on for him so wants to know where we are as he works out investment and media issues with the project. I don't mind so much sending the reports because I don't believe it's a reflection of our working relationship one way or the other (ie - I don't feel like he's checking up on us...). If it makes him happy then so be it, and it's another entry on the invoice so I'm not losing anything in the process.
If you feel like your client's need for info comes from a sense of insecurity on her part you might want to try opening a dialogue about it to find out what you can do to help her feel more at ease with the virtual setup - a lot of clients who are new to the virtual world feel uncertain that the work they're paying good money for is getting done. It also could be that she'll back off after a while, once she's more comfortable with you. How long has she been with you?
It may be that she's just really tentative right now and doesn't know any other way to communicate or alleviate that. Use your amazing skills in diplomacy to draw her into a conversation about it and you may find she relaxes quite a bit.
Can you elaborate a bit more on what it is about the reports that are making you feel unhappy with the situation?
There are all kinds of clients, some will let you run with their ideas and your own and you'll rarely hear a peep from them. Others require a more in-depth relationship and lots of communication - and then all the other 'types' in between
Getting to understand how to handle each client's individual style and preferences is a skill that takes time and isn't always easy to learn in some cases.