In my experience of having chickens access my compost pile, is they'll pull out the whole contents in search for worms. Personally I would plan to have the coop separated from the compost pile, especially if you're building a movable tractor - are you planning to somehow move a flock between a tractor and their coop every day???
I love to compost, and I actually use the chicken area as a very large compost pile - that's how my 2nd chicken run is setup. It gets lots of yard waste and organics dumped in (arborist wood chips, hay bales, leaves, grass clippings and yard rakings, all my kitchen food scraps, etc. to promote more worms and bugs for chickens to forage daily as a boredom buster. And then after time, you can rake aside the chunks and shovel out that beautiful topsoil underneath for gardening. The soiled bedding directly under where they roost, I transfer to the compost pile to hot compost once per year.
As for mesh floor -- Chicken wire is very porous and would not be a great choice for floor of a coop vs chicken feet; it would be better to use tighter mesh 1/2" hardware cloth - but even at 1/2" it's still will prevent poops from passing through, and give you chores of dry poop scraping on mesh, not fun. I use a small cage for chicken jail, and I think the floor are 1x1/2 mesh, which allows more poop to fall through. IMO the better choice is to use a deep dry bedding system under roost areas, top off with fresh bedding now and then, and do big clean outs to reset after like a year's time.
Good luck!