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What incentives do the coordinators have to take on what seems like a lot of work? How are they compensated?
They take a small fee from both parties on each transaction. Most of the time they don't need to do anything other than maintaining the service up and running. In the rare cases were ther is a dispute, they might need to intervene, but it's usually (in my experience) not a lot of work (time) either.
How private are the chats? Some people I'm transacting with have suggested we move to another platform or transact through email. I haven't done this, and I am weighing the different op sec of different methods.
They are always encrypted. A little more info here.
I think you've already got the rest of your questions answered by others. :-)