anumber1

U joints. The lift adds a lot of angle to the rear driveshaft.

It is a cooling fan and its not a problem. The fan will shut off automatically or when the BCM goes into "sleep" mode after 20 mins.

Clean the connections! That ground looks terrible in the picture...

Yep. This is a cheap example. Probably fine for occasional use. I have a K/D version of this tool and a 3/8 drive, "crowfoot" version. http://www.harborfreight.com/78-in-Oxygen-Sensor-Socket-69022.html I really only use the "special" tool to install a new sensor. I clip the wires on the the sensor to be removed and use a standard deep well socket or box end wrench most of the time.

O2 sensors definitely have a finite lifespan. Even if they "work" enough to not throw a code, they get "lazy" with age and miles. Typically, you can back probe them to see how fast/well they are cycling (measuring in milivolts). So, yes, in short, you can improve mileage if you have slow/lazy sensors. I treat em like tune up parts. Change plugs, change at least the upstream o2 sensors.

Looks a lot closer to $200 for all 4 sensors. And that would be buying the most expensive parts at Rock Auto https://www.rockauto.com/en/catalog/chevrolet,2005,silverado+1500,5.3l+v8,1431121,emission,oxygen+(o2)+sensor,5132 You mentioned you were all about the fuel economy. Nice, fast, fresh o2 sensors are high on the list of making your truck run as good as it can. That would go much farther than removing your catalytic converter and continuing to run your ride in a poor state of tune. Regardless of whether or not you decide to remove your emissions equipment or not, getting your truck to run to perfection is the best way to ease the pain of low miles per gallon (or turn your 33"s through the bogs or across the desert). While you are at it, a nice, clean MAF sensor is pretty important also... It's not like it's 1981 anymore. The cats on your truck flow pretty good, rarely go bad unless abused and with a stock motor, you will not realize much in performance gains pulling them. Have you been running your truck with a bad misfire for a while? Do you go through a lot of oil? If so, then the cat may really be dead.

Could be the o2 sensor after the cat is bad. If you are dead set on removing the cats, your are gonna have the light on anyway unless you get a custom tune. If the truck is your driver, not just a mud toy, fix it and keep the cats. More than likely, all 4 o2 sensors could be tired/lazy. Fuel economy? 33" tires and a lift? Funny stuff...

The rubber, flexible brake hose attached to the caliper may be deteriorating internally. The hose will not allow brake fluid back out of the caliper when you let off the pedal. As the dragging caliper heats up, the pressure builds. Also, with every stop, the pressure also increases. Eventually, as you have experienced, the brake completely locks up. The master cylinder may also be the culprit but I would personally start by replacing the hoses.