A:
Well, yes, it can be wired to the brake circuit but chances are the first time you used it a combination of the following three things would happen:
1. At best you would blow the fuse to your brake lights.
2. You will cook your brake light wiring and maybe more.
3. At worst, real expensive damage would happen to your vehicles electrical system.
As near as I can tell this winch has 30 amp protection and a set of alligator clips. The only real way to hard wire it is to run the appropriate sized wiring between the battery and winch plug. Same concept as your trailer light connector but with 8 gauge wires and bumper plug for the winch.
Wiring kits I have seen start at about 50 bucks.