At this point in 'Time', I've no idea what is Canon and what is not - I think the 'Time' for that is long past. I have watched Doctor Who a long while though, and while I did believe that Susan was his grand-daughter, I did often wonder about her mother. And also, Susan never quite seemed to be a Time Lord, so the possibility that she was part-human was quite high.
Now, nowhere does it say this is Susan's mother, but it is unlikely he has too many daughters around. So who knows?
As for the Mother, didn't that woman in the Doctor Who Movie (with Paul McGann) get closer than most. And the Master was there at that time.
As for the ideas expressed about the Master and the woman with red finger-nails - there is still the strong possibility that the Doctor and the Master are brothers - making this new daughter the Master's niece, and Susan his grand-niece.