Which is the proper speed to be maintained during a Forward Slip? Near Vfe or Vref? Which one will let you lower with the shorter ground distance and why?
Vfe is quite fast to be flying on a landing approach slipping or not, although I suppose there's nothing stopping you from doing that if you need to dive that steeply. You still end up with excess energy and will land long. What matters in the end is your energy state as you get to a few feet above the ground crossing the threshold.
A moderate speed safety margin above landing flap approach speed is sufficient. Keep in mind that a calibration error is created when the pitot is angled off the airflow and the airspeed will read a little lower than when straight.
If I'm approaching at 70kt and start slipping to lose altitude, I push over a bit to bring the airspeed up to 75 or 80 kt during the slip to have some safety margin against stall/spin. As I get close to the surface, I'll ease the nose up while keeping the slip in to bleed off the excess speed, then straighten out, more or less in one motion.
If I really messed things up and find myself too fast/long as the flare is coming up, I'll keep the slip in place right into the flare, straightening just before touchdown.
In the end, you slip at the lowest speed that is safe, only going faster because you need to dive more steeply, and are aware that you will arrive at the threshold with excess energy that still has to be dissipated.
First and foremost is safety. There is no general answer because each aircraft model has its own safety margin when flying cross controlled.
Seek expert advice, and always try the slip at altitude first.
Consistent speed is important for judging approaches because aircraft kinetic energy is proportional to the square of velocity. Excessive speed can really butcher an approach.
With the Cessna 172 I was lucky to find that forward slips could be done at my favorite approach speed: 65 knots. That is exactly 1.3 of the flaps up stall speed of around 50 knots.
This enabled a forward slip with out any great change in approach speed. Just used it when a little high. Rounding with excess speed can have one floating down the runway for an uncomfortably long time.