Hi walter1--Correct wheel bearing adjustment: Tighten nut hand tight, or lightly with a wrench. Spin wheel to smooth out grease. Grab top and bottom of wheel and shake. Should be no looseness. Loosen nut one position and line up holes in spindle & nut. Grab top and bottom of wheel and shake. Should be some looseness. If not loosen one more position and shake as before. If looseness detected install cotter pin, and dust cap, and you are ready to go.
Inside tire wear might be wheel to loose, or alignment problem like a bent spindle.
Trailer brakes lock in reverse may be a brake controller incorrectly connected. Some controllers disable brakes when in reverse to improve low speed backing up. That line may be connected to a hot line in error.--Frank S