Goal is to Distribute the Load
1. Yes, in most cases it is necessary to use a backing plate for any motor mount holding more than a trolling motor. The goal is both to eliminate punching action of the bolts and to add rigidity locally to distribute the load of the motor levered out on the bracket to a large area of the transom. Look around your boat; you should find that bolts holding small items (light fixture) have just a washer, larger items (halyard block) have an oversized washer, substantial items (lifeline stanchion) have a backing disc or bar, big load stuff (motor mount) has a backing plate. Replacement motor mounts will have recommendations based on their capacity. My bracket instruction limits the load allowed (both motor weight and motor Hp), specifies the bolts, and requires a backing plate mounted with marine adhesive for any transom less than 2" thick. My plate is marine plywood, as most posts here have previously noted. 2. Longitudinal stringers are like adding ribs to the structure of the transom. This may be a temporary solution for a weakened transom in tough shape. Conventional mounting assumes that the transom is sound and not cracked or rotted. They are not inherently weak; they are designed for the overall load and need to have the local bracket load distributed a bit. If the transom structure is sound, the backing plate is the right solution.
