Gravity travels at the speed of light (the speed of causality). If the sun suddenly disappeared, the earth would continue orbiting around where it used to be, for about 8 minutes.

Nothing can travel faster than light through space, in a vacuum. However, if you pick two points in space that are far enough apart (e.g. at opposite sides of the observable universe), these points will be moving apart faster than light, because space itself is expanding.

The expansion of space isn’t coming from a single point outward, like an explosion. It’s expanding by the same amount at every point in the universe. People analogize this in lower dimensions to stretching fabric or blowing up a balloon.