Hello, welcome to the forum

Firstly, regarding the JR Pass. As far as Im aware from when I purchased mine last year, the JR pass did not cover trains for nothern routes. Their are specific 'lines' that are represented throughout the country, the JR pass (well that I had purchased) covered from Tokyo all the way west and south west into Kyushu region. Im very sure it was possible to get JR pass for northern routes and to Hokkaido, but was a seperate pass.

Regarding the expense of Domestic flights Hokkaido,depending on which airline you choose will depend on the price. But you will be looking anywhere from 17,000 yen to 34,000 yen for a one way fare (sorry I can't be more accurate on price, the price depends on the airline).

In terms of travelling by Shinkansen (bullet train), the Journey could take approx 3 hours

I haven't been to Hokkaido though so I cant make any comment or recommendations regarding it, would love to go there though