On Claire’s summer Pod Tour of America, she mentioned that she wanted to shadow one of the directors (can’t remember if she mentioned Lesli specifically), just so she could get a better feel for everything else that goes on in the production. But she said she doesn’t have a great desire to direct. She just wants her husband Hugh to direct.
As for your last question, I have no idea whether they’ll let Maury direct (and I don’t think him returning as Max is even a requirement). They seem to be using the same group of 10 or so directors every season the last few years, and it’s possible that since so much else changes with their production every year–from the crew to the location–it’s nice to have that kind of consistency.