1. For me it took 2 full days on bus with a nights stop at the border at Belahiya, because it was the monsoon (late May) and we had to go slow on those winding mountain roads (As an aside travelling by bus from India to Nepal is quite an experience, especially if you have a fear of heights). I booked with Paul Travels leaving at 8 in the morning from Varanasi and reaching Belahiya (Border) at 8, walk across, get your passport stamped (Indian side is a small shopfront, Nepali post is a pretty little cottage, you'll find it, just follow all the other travellers. In any case the only way you can walk is forward to the border.)
The next day again 8 to about 6 or 7 in the evening, reaching Pokhara. Kathmandu maybe 2 or 3 hours later.
2. Assuming the Chinese keep Tibet open, the many travel agencies on Pokhara's lakeside or Thamel in Kathmandu can do it for you (and that's pretty much the only way). The catch is that you have to be part of a tour, which can be expensive although "budget" tours on jeeps have become more popular these days. When i was there this time last year (Tibet just re-opened), 10 day tours were almost a thousand USD.
3. Ill assume you mean from India to Nepal... Its about 300 USD, maybe a bit less, to fly from Delhi to Katmandu.