You can't go by public transport from Haifa to Nablus. This question has been asked before. Unfortunately the search function isn't working, due to maintenance problems.
As far as I know there is no crossing from Israel to the northern West Bank that is open to tourists travelling by public transport or taxis. The problem is that Israeli cars cannot enter cities under Palestinian control, of which Nablus is one, and Palestinian cars cannot enter Israel.
Perhaps someone on this forum has done it recently and knows more about it than I do. I am Israeli and am consequently not allowed to go to cities that are part of the Palestinian Authority.
You can go from Jerusalem to Nablus or vice versa. Arab buses and shared taxis leave from the Damascus Gate in Jerusalem. It may be necessary to change in Ramallah. Again, others will have more information on this than I do. This one is certainly easier than Haifa to Nablus.