Official sermons, and my ignorance

There's been a lot of stink about Rick Warren delivering the Invocation the day of the inauguration of our next president. The result of that controversy is the choice of Reverend Robinson, gay minister, to do some kind of kick-off prayer.

My questions:
a) Is this official state business paid for by tax dollars under the justification that the new prez has the choice to have his faith be a part of it? If so, how is this happening? Shouldn't the financial burden be shouldered privately?
b) How many prayers are involved in the inauguration?
c) What's the difference between them?
d) What, exactly, is Rick Warren invoking?

I confess complete ignorance about all of this. I'd appreciate help in understanding the role of prayer in the Presidential inauguration.

Ricky Gervais weighs in

The debate is over.