Hi, I'm James. I want to help you resolve these problems. A couple questions first:
1. Is the vehicle still under warranty-if it is I would suggest seeing dealer?
2. Can you supply the VIN#?
3. Are all these fuses in the underhood fuse block?
4. Do the light fuses only blow with trailer connected?
OK, thank-you for the additional info.
1. No, the drivetrain warranty does not cover these problems.
2. The simplest of these problems: cig. lighter/power outlet fuses usually blow when inserting accessory plugs or if someone inserts a metal object and shorts outlet. When insert accessory plug, take care to insert it straight and without too much force.
3. Now the big problem: Maybe you have tried this but I would unhook trailer and check if backup light fuse blows then. If not, problem is with trailer (most common). If is still blows, problem on vehicle. Here is a schematic of backup lights: for your info-I don't know if you will find it useful or not.