Speedbump + Taillight

Maybe, maybe not. Impossible to say for sure. If the turn signal failure happened immediately I'd be more inclined to say there's a relationship.

A new turn signal bulb is a few bucks at the local auto parts store. They might even install it for you.

If you install the bulb yourself DO NOT touch the glass part of the bulb. Finger prints shorten bulb life.

I doubt it. Bulbs burn out and have to be replaced all the time.

The physical shock to the buld filament due to hitting the speed bump was minimal because the filament mass is low and the suspension absorbed most of the impact.