Your payload capacity is 1560 lbs. Your tongue weights will be around 840-1260 depending on if the tongue weight is 10-15% of the total weight of the TT. I point this out because you don't want to have too much weight inside your truck....every accessory added to your truck is deducted from the 1560 figure too, step bars, spray in bed liners, bumper guards etc. Once you know you're not going to exceed your truck's GVWR (7,100 lbs)....you're almost ready to tow.
Do you have a good weight distributing system (WDH)? Of course use the tow mode. Cruise control is not recommend for towing beginers.....but if you do find yourself on a desolate stretch, it won't hurt anything. I can't help with gears though, except it's wise to lock out 6th with that much weight. Being in 6th gear in and of itself won't hurt anything......but if the transmission hunts constantly between 6th, 5th, 6th, 4th etc.....it's a bad thing. That will create a lot of heat, and something will break eventually.