1) Yes, stones would help, or better surfacing near the shore/beachy area.
2) I think it's not the trees that are the problem, it's... again... surfacing. Trees don't normally just sit around on rocks like that. The floor near them should have dead needles, sticks, ground cover, etc... Since that's not so easy, I'd recommend adding some surfacing under the trees, ground cover, or bushes.