Tow kit installation from 98 to 01

I recently purchased an 01 after totaling my 98 in a collision with a deer, long story short I am trying to figure out what I want from the 98 before I have to get rid of it. My 01 does not have a hitch so I am assuming it does not have the tow package. I am thinking about removing the hitch and wiring off my 98 and installing it in the 01. I have a few questions:

My 98 has a hitch that is wired that seems like its from the factory, does this mean it has the tow package? How do I find out for sure?

Does anyone know where I can find info on installing the hitch and wiring?

I understand that the tow package also includes transmission cooler, engine oil cooler, 130 amp alternator, and heavy duty battery.

Are these things I can remove from the 98 or would it be easier to buy them separately?

If I install only the hitch and wiring, what limitations will that put on my towing ability?

I had a trailer in the past roughly 4500-5000 lbs which I towed with the 98, not a pleasure to tow but it got the job done. I don't have a trailer now but I would like the tow package on my 01 to increase value and to have the option in the future for occasional towing.