Deep litter can be used in some coops but generally works better in a run since you want the litter to interact with everything from moisture to microbes to worms living in the soil.
Free ranging always carries some risk but yes it is nice to let the chickens get some free time. I only let...
1&2) Any reason why you want deep litter in the coop instead of the run? Do deep litter in the run after the grass is gone. But I wouldn't do it in the coop unless it's well set up for that - how large is it, what kind of floor (I assume directly on the dirt?), etc.
I just use wood chips in...