I don't know how a 'historian' could have gotten that one wrong. This is pretty basic to the story line of 1066.
Yes, that's true. I just excerpted the article.
Hardraada probably had something else in mind in the long run; he was supposed to be awarded Northumbria had they succeeded, but given his history, he probably wouldn't have stopped there.
There's a cool anecdote from before the battle -- as a reward for supporting Harold, Tostig would have been given the lands north of the Humber. When Tostig's party asked what Hardraada's share was to be, the herald said, six feet of English ground, or however much more his height would require.
And then it was on. ;')