Once a year. However, for areas that get a lot of traffic this may need to happen more regularly in order to keep the vinyl flooring looking its best.
Depending on the condition of the vinyl, there are two basic options. First is a deep scrub of the vinyl to remove surface soiling and then re-coating. The second is stripping off all the wax and then re-coating.
Scrubbing and re-coating involves removing only the dirty layers of finish and then applying coats of finish on top of the clean floor. This process capitalizes on previous coats of finish and gives the maximum appearance possible. If a floor is scratched and marred beyond the point of successfully scrubbing and re-coating, then stripping is the only viable course of action. Otherwise, scrubbing and re-coating is always preferable because you get to take advantage of the previous coats of finish.
Outside of VCT, vinyl does not need a finish. The only time a finish should be put down is if the floor is going to take heavy traffic or equipment being moved on it. A finish could be used as a sacrificial layer to protect the vinyl
This depends on the flooring and where the scratches/gouges lie and how deep they are. For VCT, surface level scratches will be removed through removing a few layers of wax/finish. Deep scrapes or gouges may not be able to be fixed.
For vinyl flooring, light scratches can be masked with a color matched furniture pencil or similar. Deeper gouges or chips can be repaired with color matched wood filler.