the doctor is still a timelord. they created timelords by replicating their dna. regenerating came from them, perhaps other things like two hearts are also something unique to them, who knows.
also who says? the doctor? whos mind was wiped? he never died on trenzalor so whos to say he didnt just THINK he had 12, or perhaps when the timelords "decided there would only be 12" they didnt somehow limit the doctor? the blast of energy couldve been the timelords playing along, or perhaps the timelords didnt even know. theyre all dead, the extent to who knew about the timeless child is probably pretty small.
we saw multiple incarnations of the timeless child, even if we exclude the morbius doctors and the ruth doctor as possibly being season 6b doctors thats still a possiblity of hundreds of years. the timelords wanted a "foudning myth" perhaps tekteun rassilon and omega were the only ones to know the truth
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we still dont know who the ruth doctor is. i firmly believe shes season 6b. inbetween 2 and 3 and part of whatever the division is.
we know shes a past doctor. thats it. her mystery is still untold, even the doctor comments on where ruth fits and still doesnt know
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before the timeline changed he died in battle but we dont know how because we never see that version of events playout only the aftermath.
river song is something that needs to be explained.