New TPMS are not needed but it would be wise to replace the valve stem. The actual sensor is screwed on by a small torx bit screw to the valve stem. You should be able to buy replacement valve stems at your local parts store but for at the dealer parts dept. or amazon.
If you can try and keep the sensors as close to the car as possible and in the same spot as you go pulled them off. If they are away from the truck at a certain distance and for a certain time then you will need to reset them. If you do not have the little computer to do it then you will need to buy on which I got mine from amazon for like 150ish or find a friendly shop that will do it. I worked at Discount Tire and we would do at no charge for people that were not even our customers. It only take 5 minutes tops and less for a person that knows exactly what to do. If your dead set on changing the whole sensor there are aftermarket TPMS that are reasonably priced. I just ordered new wheels and TPMS that ran me about 27$ each on amazon.
Tire pressure is dependent on the ply rating of the sidewall. The standard plys are 4 and then you have 6, 8, 10.
4 plys are usually 40-45psi max, usually run at 32-35psi normal driving conditions
6 and 8 ply are less common tires.
6 plys or C rating 45-50psi max, usually run 40psi normal driving conditions.
8 ply or D rating 55psi max, usually run 40-45psi normal driving conditions.
10 ply or E rating are 80psi max, and usually running 50-55psi normal driving conditions.
Some of my numbers may be a little off but for the most part that's a basic understanding. As with any tire if you have extra load in your vehicle then ramp up the psi in the tires. More psi the more weight they can handle at a higher temp. The max weigh per tire is also printed on the sidewall along with , max psi, speed rating, load range, etc. Also keep In mind the size and weight of your vehicle dry (no load at all). This will be normal driving conditions. You can play with your psi between the front and rear some but not too much as long as you don't go too low as stated above or too high, and obviously not above max psi. Too low of psi will cause bad wear on your tires and fast, will also cause you to have horrible steering handling, and will also decrease your fuel mileage. Too high of psi will give you rough rides, also effect your handing, may effect steering at high speeds, and keep In mind weight with or without load. Without load high psi bad with load high psi ok. High psi can also affect fuel mileage and tire wear.
No real info on the 20s and tire size I am kind of in the searching for that info as well. I am running the factory tires size at the moment but from what I have read if you have one of the standard leveling kits then you can usually run 33s with minimal issues. Like trimming the front bumper and/or fender flares, running boards, and pinch weld. These things are pretty easy to do even for a newbie. Just look up some youtube vids and this is an easy fix.
Good luck, hope this helps some.