Upon a head, a branching crown, Shed yearly, then regrown, What bony structure's widely known?

I hope we don’t bug you, we just want to get by. With six legs that scurry, or wings to help fly. I’ve seen how you treat others of my own kind, by slipping the letter P, three spots after our eye.

Crickets have friends don't they though these can be much bigger

On a domesticated beast who travoises mountains for lush fields. Im simple in design but with a mighty job. To locate the beast who bears me. A harmonious song with no voice, I sway in stride side to side.

Tides obey, luxury's sway, Gentle rocking, wealthy play, Ocean's path, a lavish way.