Bran is the trueborn son and rightful heir to Winterfell.
True, but I think he’s probably okay with giving that up now that he’s the new “three eyed raven”. He never wanted to be a lord in a castle anyway.
Yes, but do not know if his supernatural visions and mission will preclude him from becoming heir. Sansa, her unborn son with aunt Ayia will eventually rule. Scouring out all bad traits Bolton in the lad. His true spirit will be a Stark.