When it comes to tires, I personally would trust someplace like Discount tire, before I would trust the dealership. Let them know the issues you are facing and ask if they can take a hard look at the balance and round of the tires/wheels.
Absolutely, take a look at some of the Bed mats on Amazon, like the lasfit. I purchased a similar bed mat, and it's much better now, I could hardly move the sand bags I put in the bed for weight.
Probably worth the time and effort to crawl under there and see if you can find any obvious signs of damage and/or abnormalities. Just to try and keep the dealership honest and make sure everything gets fixed.
Easy Mod and gets that big ugly low hanging tailpipe out of the way. This took about 10 min. Best advice I received was jack the suspension up a ways from the hitch (no need to lift the back tires off the ground). I didn't even have to lower the spare tire.
I don't change very often back to the Toyota Interface, I almost exclusively stay on the Android Auto Screen. When I do I get that done as you say clicking back to the All Apps, and then the Toyota App. I prefer to have the real estate on the screen for android Auto. If it was able to be ran...