Pretty much. But, towing/hauling heavy loads in overdrive generates a LOT of heat, and tends to smoke the already weak overdrive unit.

No factory hitch chances are 7800lbs is max.
You really want a good cooler for it if the trans is going to survive
Also recommend a wt distribution hitch, it will make towing a fair bit better.

If your towing a 7000lb trailer somewhere that is completely level/flat then it will do it, just not well.
If you are going anywhere other than flat/level ground, its going to struggle going up hills & could be scary coming down.

2500 would do a much better job IMHO & make your trip much more enjoyable as well.
Im a believer of having too much truck for the job as opposed to too little.

This is a good chart to give you some good general information about your truck to show tow and load ratings.
http://dodgeram.info/2001/towing-charts.html

Nice site...it lies though because it doesn't have my color listed

would be advisable to have trailer brakes and 4.10 rear gears if your not getting a 2500.

I haul my 5500 wet lb trailer, and 2 400lb atvs on an above the bed rack. I'm not the first one there, but I get there.

I'll put it this way, u have many people doing more then what your going to pull...

dont dought ur truck. u have a class 5 hitch..

Get a tranny cooler, and get rid of ur check valve ( DIY found in search) and ur truck will be fine.

Ur time tested 5.2 will pull just fine hills or not. The brakes may suffer a little but keep the O/D off, and u shouldn't be goong down to steep of a hill the downshift won't do it