When backing out and switch to Drive, it hesitates before engaging. When I go up a hill, it makes like a weird "thunk" sound like its in the back the rear wheels. Lastly, when cold, the shaking while idling is awful. Doesn't do it when warmed up.

 

Your question will be better answered in the Ranger forum here https://www.ford-trucks.com/forums/forum35/

Is the ATF full? When was the last time the plugs were changed? Is the air filter completely clogged? Have you changed the fuel filter lately? Is there a check engine light?

 

Welcome to FTE.

Would be helpful to know which engine & tranny you have, if it has the two piece drive shaft, how many miles on it & where the vehicle is on All past & present due Ford scheduled maintenance replacement items, so ^+1 on the above suggested beginning checks & post the results.

Scan the vehicle computer/controllers for trouble code clues & post All code Numbers, as they can help focus a trouble shoot. If you don't have a scan tool, or have a friend with one, most auto parts stores will scan at no charge if the CEL is lit & some will scan even though it isn't lit, if we're having problems.

Did the problems come about slowly over time, or suddenly after some event???

Some beginning thoughts for consideration, let us know what you find.