An equalizing hitch has lift bars that transfer some of the trailer's weight to the front end of the chassis. The full tongue weight of the trailer is not carried solely by the rear end of the vehicle. You hook everything up, then pull up the lift bar chains with a pry bar and your truck magically becomes level with the trailer.
In this pic I was carrying about 3000 lb of trailer (motorcycle trailer borrowed from my bro-in-law) and my kids' stuff with the factory Class II hitch, no equalizer, moving them from my ex-wife's place to mine, about 400 miles. You can see the rear end is a little low, but not too bad. For a 3500 lb boat I wouldn't worry about it unless you tow the boat on long trips. When we started here I had a hitch-mounted bike rack installed into a Class II to Class III adapter, then the trailer attached to a ball on the bike rack. Probably illegal but wife #2 insisted since she bought me the bike rack. The extra leverage exerted on the adapter by the bike rack bent it by about 30 degrees before we got out of town. Therefore I don't recommend using an adapter for actually towing a trailer.
A brake controller connects the electric trailer brakes to the tow vehicle's braking system. It will modulate how hard you are hitting the tow vehicle's brakes and apply the trailer brakes accordingly. Professional installation required. Most boat trailers with brakes use hydraulic surge brakes (electric anything + water = bad) where the trailer's brakes are controlled by a master cylinder on the tongue, and you don't need a brake controller. When you brake the tow vehicle the hitch senses it from being pushed against the hitch and applies the trailer brakes. Rental trailers work the same way, to avoid having to install brake controllers on a lot of vehicles that may only tow a trailer once. No special hookups for surge brakes other than a safety release.
Towing requirements vary by state but as I recall, once you're over 2500 lb every state requires trailer brakes of some type. The only thing I regularly tow is my jetski, and ski, trailer, and a full tank of gas is only about 1000 lb so I don't need trailer brakes.