In the movement of planets what is the movement of gravity?

Grqvity creates and acceleration field that accelerates the Planet m with acceleration equal a=GM/r2 = v2/r . This acceleration results in a force on the planet of f=ma= mGM/r2

Orbit

Orbit around another body, rotation around its axis.

Any object in orbit moves fastest when closest to the primary, and slowest when furthest away. That's a fundamental part of Kepler's laws.

Yes. The planets would sail freely off into space if gravity weren't always pulling them back toward the sun.