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I get a 'thrumping' noise after starting the engine.

Sounds like you may have a sticky injector, when the engine is running loosen the fuel line to the suspect injector, if the noise stops then you have the correct one. Once you have isolated the bad injector swap it with another one and see if the noise follows. A stuck injector is indeed a horrible sound, very deep knocking.

I'm Getting a funny noise coming from the engine.  It sounds like the lowest pulley is (loose?)  and making an intermittent squeak/click noise.

It's your Harmonic Balancer pulley. Mud gets packed behind the bearing and causes the bearing to go out causing it to wobble (yet another reason why deep mud is dumb) $80 bucks for a new one. 15 minute fix.

When I shut the engine off I hear a clunk.

If the rubber in the vibration damper tears it will slap back when you shut the  engine off. This damper reduces vibration in the crankshaft and associated moving parts created by the torque of the engine running. A bad damper must be replaced ASAP. When it stops working correctly, the engine main bearings, crankshaft, and block are stressed. When over stressed, they may slap you too--but much harder, usually in the pocketbook.

Had a strange noise coming from the engine area under low RPM and light load. Turned out that the (serpentine) engine pulley was worn out.  The rubber gland was toast. Got a new one at the GM dealership, its part # 12557345

Continuous chirping cricket sound inside the cab.

I discovered if I held down/ slightly pushed the emergency brake or the T-lock shift, the noise temporarily goes away. 

I diagnosed the problem by driving down the road and having the power steering pulley fall out. This is a typical problem when the power steering pump shaft breaks.

You hear a "snick snick snick" sound, and squeaking when the Vacuum pump seizes and your pulley quits moving.  You should be able to see this at idle.