Little or no power when placed in reverse gear.

check the width of the chassis rails for starters . If the same width then check the cab mount distances . With 9 years between chassis I would think that the chassis will be different

Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as-------------------------------------------------------------------------
car cables & obd conectors

1. check your fuel filter and replace
2. this sounds to me like you are losing power due to your valves being out of adjustment, valve lash adjustment should be checked at every tune up on this motor
3. a manual on this vehicle would be a great asset to you

assuming truck shifts into all forward gears, synchronizer broken or shift lever damaged inside transmission housing.

If it seems to run well otherwise, you might have a partially obstructed catalytic convertor. Usually if this is the problem, the engine will also bog down even if you try to rev it up when it is in neutral.

No difference in transmissions at all between single cab and extra cab.

bad clutch

if you have a manual or a trouble shooting book, locate the wiring diagram for the headlights, sometimes there is an in-line fuse or relay located on the vehicle somewhere. there has to be a fuse somewhere i promise. start from the headlights, try to chase back until you get under the dash. normally the wiring will be bunched up into a (compact type) or bundel, worse case senerio, split open bundel to expose all the wiring. there is sight that may help you. autozone znet.com

try and start truck and once started let key come back a little bit and let me know if it stays running

With the vehicle sitting still, ease the clutch out just a little bit while trying to engage reverse. If it pops in, even with a little grinding, it seems the bearings on the counter shaft may be a little stiff. Have you checked the level of the gear lube in the transmission?