Yes, the child tray is removable.

Only regular breaks on the back wheels. No grip breaks.

yes. they are inflatable.

My daughter is 37" and is only in the second of 3 height positions for the shoulder straps but the top of her head is only a couple of inches from the top of the backrest. The backrest measures at right about 17" high but they also do sink down in the seat a little. I hope that helps!

It does ok, better than my regular stroller did! It does take some effort to push through the sand. But then again it may depend on what kind of sand you're pushing it through!

I don't know the exact distance, but the footrest thing stretches out in front instead of down so your son's feet shouldn't touch the ground.

No, the seat does not lay all the way back. This stroller is designed for babies 6 months and up but it comes with a carseat adapter so you can use your carseat if your baby's younger than that. The farthest the seat goes back is about the farthest a seat in a regular stroller goes up, if you can picture that. My son still naps in it comfortably though. And I don't know how big a diaper bag you're talking about, but it's a pretty decent sized basket, there's plenty of room.