Broadly...

MixTape's hosting is metered using "hosting credits". Each of these credits represents one "download/minute". I.e. if one person downloads a five minute mix, that uses five of your hosting credits. If five people download a ten minute mix ... fifty hosting credits. There is also a minimum charge of one credit per stored minute per month.

How many do I have?

If you bought MixTape Lite you will have an initial hosting allocation of 2,000 download/minutes. This is enough for a few mixes for a few friends. Pro users have an initial allocation of 20,000 download/minutes. This is heaps. Additional hosting can be bought by selecting "Buy Hosting" from the MixTape menu or going to the Licensing tab in preferences.

Hosting is US$20 for batches of 20,000 at a time.

How can I see how many credits I have? See which mixes I'm hosting? Remove or rename a mix?

Go to the MixTape menu and select "Manage Published Mixes". The drop down that appears shows all your hosted mixes, their lengths and the number of times they have been downloaded as well as (at the bottom) a statement of the number of remaining hosting credits you have. To view, rename or remove a mix right (or command) click the name of the mix.

Is there a log of what I've been billed for and when?

You can see from MixTape itself which mixes have been downloaded the most but other than that, no. In reality the amounts involved, for almost all users, are tiny.