Can I turn the running lights off of my 2005 tahoe

check blower motor resistor connector could be burnt or resistor it self

That is just like a 2005 buick century, and it is normal. When you open the driver's door, the radio turns off. Does yours turn off too?

http://wiki.answers.com/Q/Where_is_the_fuse_for_the_third_brake_light_on_a_2005_Chevy_Tahoe

You may have to have the radio rewired to not run from main ignition, therefore allowing you turn off your lights without loosing the radio.

GM OIL LIFE SYSTEM - RESETTING
Reset the oil life monitor when the oil has been changed, use the following procedure.
1. Turn the ignition key to the RUN position.
2. Fully push and release the accelerator pedal 3 times within 5 seconds.
3. If the Change Oil Soon light flashes, the system is resetting.
4. Start the vehicle.
5. The oil life will change to 100%.
6. If the Change Oil Soon light comes back on, the system has not reset. Repeat the procedure.

Grinding noises are a big concern. get it checked out ASAP.

A new blower motor resistor

do an electrical check of all wiring to all the lights, you are describing the symptoms of a bad ground , bu i don,t have enough info to gues if its front or rear,

Open tailgate and there will be 2 screws that hold light housing remove and then turn the light socket out that you want to replace. Turn it 1/4 turn counterclockwise. Replace bulb and housing.

Depending on what type of trailer you have, a blown lightbulb on one marker could kill them all (like the old Christmas light strings). Look at those, and make sure your ground is good.