For the Tire, I'm thinking - Damaged Axle or Spring/Spring mountings. Pretty easy to hit something way back on a heavy trailer and not feel it.
The Brakes - Call Tekonsha - Cequent Performance Products
(800)632-3290
It seems the brake controller doesn't know that you're braking. Some of their controllers have lifetime warranty so they might just send you a new one. The only one I've actually used was a Tekonsha Voyager, a very "entry level" unit. Works fine, just not very user friendly. We had a case here where a Voyager wouldn't respond to stopping and the little pendulum inside had broken off. I don't think Prodigy series uses a pendulum but don't hold me to it. Tekonsha's tech people are very helpful.