Hi Chong Thaw Sing,
1.) Yes the train trip to Hokkaido is completely covered by the JR Pass. Note that it does take a good amount of time travelling all the way from Tokyo - Hokkaido, so it may be nice to plan in a stop or two on the way.
2.) Anything is fine, it depends what you wish to experience. Winter is great because you can enjoy the Sapporo snow festival and lots of other winter spots. If you wish to see more of nature then late spring makes for a good time. Summer is also good because there's no raining season and the weather is generally better in Hokkaido than the rest op Japan.
3.) The JR Pass is good for travel to and within Hokkaido. You would also be making very good savings over normal tickets when you make the trip.
Hope this helps!
Daniel