1.) Ticking noise upon start up. Usually lasts for a minute, then goes away.
Exhaust manifold gasket, most likely. Mine did this for the entire time I owned it, I never bothered repairing it. Maybe start it with the hood up and see if the sound is coming from the driver's side of the engine, that's your exh. manifold.
2.) Exhaust smoke coming out from in between bed and cab. (assuming this is an exhaust leak that I can patch).
I'm sure it is (an exhaust leak.) There's a flange between the downpipe and the catalytic converter pipe which is prone to become cupped & failing to seal, even if you replace the gasket. But that's just a guess - it could be anywhere in the system. You can start it and immediately scoot under there and run your hand along the pipe (without touching it, of course) and see if you can feel where it's leaking. Should be obvious once you find it.
3.) Upon start up, it will rev to 2000 rpm for about 30 seconds. I have seen multiple threads on engine revving, but what exactly is this caused by?
Faulty throttle position sensor, or maybe a grounded wire to the sensor. Try unplugging it and see if it is consistent or changes. It's the green (and white, maybe?) wire that runs along the passenger side of the top of the engine (valve cover) to the throttle body.
4.) When depressing accelerator at low speeds (5-25 mph), there is a slight ticking noise until I hit a certain point, then it
subsides and eventually goes away.
Could be valvetrain noise, you don't have a lot of miles on the truck but it could be worn enough to have a little trouble getting oil all the way up to the cam. Try using full synthetic oil at your next oil change, if you don't already use it. Full synthetic works into the pores of metal (yes, metal is porous at a molecular level) - sometimes that's enough to create a sheen of oil that can overcome weak oil delivery up in the top of the engine.
5.) When accelerating up a hill or hard acceleration, there is a noise coming from the manual transmission gear shift area.
Eek, this one eludes me - what kind of noise? You might want to remove the shifter boot so you can hear it better. When was the transmission gear oil last changed? If you don't know, maybe change that & use something quality - again full synthetic is good. You could put some Royal Purple in there and never worry about it again.