Why did he grow the arm?

Because Adam Rifkin got high in front of a typewriter.

Evolution, plain and simple. It would have upped his productivity as a garbage man in order to stave off the wage depressors.

Nah, just kidding. He did it on purpose to piss off his mom.

As a garbageman, Marty was exposed to garbage that must have mutated him by giving him a third arm. However as a comedian he wasn't around the garbage so the arm just vanished due to the lack of exposure to garbage. I hope this expains things.

garbagemen have a much higher rate of cancer and other exposure related illnesses than the general public.

Because he picked at it.

Can't stop the signal.

Pretty sure some chemical sludge spilled on his back while he was collecting garbage.