1) Difficult to say as your "hard" may be different from mine. For a (very) short ride, try some of the wee tracks round the Quirang. Just drive up to the car park to save yourselves a bit of ascent. Short, but stunning. Otherwise, head down Glen Sligachan as far as the weather, the track conditions allow and just head back to the dry and warmth when you've had enough.
2) Pick a mountain, any mountain! I recommend the book "Skye Scrambles" by Noel Williams. All the routes are graded and the way-finding is very specific ("turn left at the 3rd red boulder" type of thing). If you don't want to buy a copy, let me know and you can borrow mine for the price of postage). Bla Bheinn probably offers the best view of the Black Cuillin and is worth it for that alone.
3) The Sligachan is the "go to" destination but I prefer to be based in Portree. There are a few decent wee pubs and a decent Indian restaurant (Venison Korma anyone?)