Welcome to the forum! You are wise to get these questions out of the way before you make the commitment. Hopefully, we can steer you right.
All of the R52-gen Pathfinders come capable of towing 5000 lbs. or more and have the transmission cooler built-in. The tow package adds in the tow hitch receiver, the 7-pin wiring harness and a harness for the brake controller (not included). The only models with the tow package are the SV and SL with the tow package option, the SL with the Premium package, and the Platinum, with which it is standard equipment. The S does not have this option available, so you would have to purchase them and install them yourself, which is doable.
All of the R52-gen Pathfinders come capable of towing 5000 lbs. or more and have the transmission cooler built-in. The tow package adds in the tow hitch receiver, the 7-pin wiring harness and a harness for the brake controller (not included). The only models with the tow package are the SV and SL with the tow package option, the SL with the Premium package, and the Platinum, with which it is standard equipment. The S does not have this option available, so you would have to purchase them and install them yourself, which is doable.