At 37,000 miles the rotors (silver round thing) should be fine.
Yes the backing plate is a steel piece that the friction material is bonded to. When you look in there you can see 1 side and if it's 1/8 of an inch, then replace NOW.
Just to be perfectly clear, ( we are talking brakes here ) the backing plate is the outer yellow piece that has the silver pin in the center running thru it. OK? The friction material is also yellow but smaller and the pin does not go thru it.
Now, we are talkin about a MAJOR safety system that keep you safe but also those around you. If you do not have the knowledge, skills or tools, please ask for help or take it to a shop and watch. I have no idea where Fountain Hills is, but if I were close I would come and help you learn this simple but very important task. Please take no risks with this work!