From the SRD:
"When flying, the creature can halt its forward motion and hover in place as a move action. It can then fly in any direction, including straight down or straight up, at half speed, regardless of its maneuverability."
Once the creature performs the initial action, it is using the hover feat and is "hovering", regardless of the optional movement feature.
"If a creature begins its turn hovering," - IMO the only way this can be true is if the creature used the Hover feat last round (movement or no movement).
"it can hover in place for the turn and take a full-round action." No five foot step, and no charge actions. Any other full round action is allowed.
Note: Creatures with flying maneuverabilty of good or perfect are not subject to the restrictions of this feat. They can take 5 foot steps with their full round actions, except good fliers cannot step upwards.