OK, I'll throw in my tuppence worth on both points.
First off, I see no reason why the Doctor can't be "non-white", whether that's black or anything else.
All we're really talking about are some relatively minor genetic changes which affect things like skin tone, hair, features ... you know, all the things that have already changed TEN TIMES.
Patrick Troughton had a darker complexion than Hartnell, Peter Davison is pretty pale, Colin Baker's hair was madly curly ... it would hardly be a stretch if a regeneration made his skin go darker than it has in past regenerations. I mean, great swathes of his DNA are essentially being rewritten when he regenerates, it's not much of a stretch to imagine this happening.
As for whether the Doctor could regenerate into a woman, I admit I'm less open to that, despite the recent mentions that it's possible (e.g. The Corsair).
For me, it doesn't make sense, because it's already been established that Time Lords DO have genders, and therefore gender roles. (i.e. they've made distinction between males and females, they use terms such as mother, granddaughter, father, etc.).
Given that, it seems like it would be quite an odd thing for those established roles to be so fluid ... "son, your mother's body wore out and she regenerated, and now she happens to be your father, just like I am. And you don't have a mother any more."
To me, the idea that they could swap genders seems to only make sense if they didn't actually have any "traditional" ideas of gender in the first place. The very fact that a species has 2 genders imposes a kind of natural order that those genders should remain fixed, in order to preserve the species. Otherwise, all it takes is for a million-to-one occurrence of everyone regenerating into the same gender to happen, and the whole species is basically extinct.