The fossil record of birds is incomplete because bird skeletons are

Bird skeletons are very delicate, and therefore, difficult to be preserved.  The bones of the birds are soft. The small animals are very prone to physicochemical as well as biological decay. This is why the fossil record of bird is incomplete and well-preserved fossils of birds are rare to find, except at a few unusual sites. 

Since a female is both xx chromosome and the male passes down the x chromosome, than the offspring would be female since a female is xx.