3. IDK Edward IV had several daughters, so Henry being Henry, and if he's anything like his father, is going to love a match on paper more than a match in actuality (see Mary Rose Tudor's betrothal to Karl V, Henry's own engagement to Catalina d'Aragona). He might see the younger girls as being suitable bargaining chips to the various families of the English aristocracy.
To marry those children to an Englishman is going to cost a smaller dowry than marrying her off to a foreign king. And not only that, it would then prevent the absorption of England by France, the Empire et al.
Since, one of the main reasons, (or so I'm told) that Henry VII married Edward IV's daughters off to his supporters, was so that you didn't have various foreign kings with big armies etc popping in for tea and taking the whole country. A way Henry could do that is to extend his family into those who perhaps have rights to the thrones themselves - Courtenay, Pole - and maybe spare a daughter for the son of Regent Arran?