Are Whitewing and Birchfall's kits really Ashfur's?

This is not likely. The book Sunrise implys that Birchfall was the father of Whitewing's kits when Birchfall said; "We've called the gray one Dovekit, and the tabby and white one is Ivykit." Although this does not explicitly prove that Birchfall is the father, it certainly implys it and the books have given us no reason to believe otherwise.