9/64" bits for wood skis and 5/32" bits for metal skis are fine (or pick based on the mm recommended by the ski manufacturere, in this case 5/32" is closest to 4.1mm).
Definitely tap if the ski has metal layers. You need a #12AB tap (try www.tognar.com
to buy one). It has to be an end-tap, which is normally the only kind of ski tap you can buy.
I would not countersink if you plan to tap. Instead, do this: drill holes, vacuum or shake debris out, then tap and again clean out holes. After tapping, you will see a slight raised burr around the edge of the hole which can easily be shaved off with a sharp 1/4" chisel. Now you have a nice clean hole with threads all the way through the topsheet.
Place a drop of glue in each hole (white glue or wood glue are fine). When you start the screws in tapped holes, begin by turning counter-clockwise until you feel the threads click, then turn clockwise to engage threads and tighten the screw. Tighten until the screw bottoms and finish with 1/16 to 1/8 turn to snug up. Resist the urge to tighten any more.
I actually tap all my skis, whether they have metal layers or not. I just prefer the control you get -- I think it makes for a cleaner mount.
As far as hole depth, you can see how much the screws protrude from the RF plate and wrap some tape on the drill bit as a stop. I can't remember if this is true of the RF plates, but many bindings have different hole depths front and back, so be sure to check (often the rearmost screws on the heel piece have a shallower hole, as skis are thinner back there). You want to drill just a teeny bit deeper than the screw requires (like 1/32" more).
Good luck! RF plates are easy to mount, so this is a good way to start DIY mounting.