Re: Was the Dr ever male or female?
The Doctor has always been decidedly of the male gender and mostly - with the exception of a couple incarnations - of asexual orientation. It least he's always seemed completely uninterested in romantic/sexual entanglements. Which, if you've ever read the book that deals with Time Lord reproduction (I'm not certain of the title right at the moment. Lungbarrow maybe?), makes perfect sense. 8 and 10 seemed heterosexual, 11 seemed omnisexual (in the sense that he was totally oblivious to gender beyond using it as a method to assign pronouns) but didn't have much of a libido. 12 has hinted a couple times at a mild, cautious attraction to Missy, but he's unwilling to explore it for, I think, obvious reasons.Though that may just be me reading into scenes something that wasn't there. And I think it quite obvious, especially in the last couple episodes, that Missy was very attracted to him.
I think we can safely say that Time Lords do indeed have male and female genders.