Christianruckh,The Hokutosei train is not coming up on
http://grace.hyperdia.com/cgi-english/hyperWeb.cgiIs it running on Sun 23 Aug from Ueno at 19:03 or has this changed? Is there a better website for schedules?
I'm not sure how you were searching, but it appears as normal in the results when I check on HyperDia. The Hokutosei operates daily, and the Cassiopeia operates on odd-numbered days in August, but as mentioned in my other reply, they are not a feasible option for you this time, so you need to look at travelling during the day by shinkansen or flying.
Do I need to pay a surcharge to travel from Ueno to Hakodate if I hold a JR pass (other than for Couchettes or Private Rooms)?
Yes. Details are given here...
http://www.japan-guide.com/e/e2356.html
Can I get off the train in Hakodate and catch another train after 12 hours to continue my journey to Sapporo, or is this considered a separate trip?
If you have a Japan Rail Pass, you are free to switch to other trains en route free of charge.
