For example: A straight road with a junction to the right.
Instead of using a no right turn restriction relation, is it possible to mark the straight road as turn_lanes: through, and would navigation softwares (plural sp?) adhere to that?
It probably depends on the navigation app. My guess, and it is only a guess, is that turn restrictions are used by the routing algorithm while turn lanes are used by the turn by turn navigation instructions. Slightly different things (creating the route vs announcing or displaying the turns for the route).
No. Movement restriction is for routing. Turn lanes are for lane guidance. Same goes for lane-change.