Welcome back!
Pop the hood and look for the extended fan shroud covering a mechanical fan connected to the water pump. If that's there you have the HD cooling. If you have the factory hitch and 7-pin connector in the back then you're set on the back side too. Trailer sway control? No, I don't believe any Liberty models came with a sway control. Jeep does recommend a trailer leveling system if you intend to tow over 3500 pounds - though plenty of Liberty owners have towed that much without the levelers.
As for the brake controller...Jeep did NOT provide an easy way to connect a brake controller. There is no adapter that can be simply plugged in to a harness under the dash that then connects to your controller.
Read through this thread for details on how to find the famous blue wire that must be connected to the controller to send a brake signal to the appropriate pin on your 7-pin harness at the hitch. Since you have the factory-installed tow package the wire should be a bit easier to find wrapped up under your dash but it will still take some digging to find it.
Are you getting a Prodigy controller?
Bob