Cecily of York had been offered to the Scots from her birth - the offer was repeated in 1486 with Cecily marrying the future James IV and Elizabeth Woodville marrying the widowed James III - it fell because of James III's death and James IV wasn't particularly keen on fulfilling the match with Cecily at that point.
A sister or half-sister of Henry Tudor is going to be in a similar position to Elizabeth of York's sisters and will largely depend on how Henry views her.
He married his sisters in law to close supporters.
His own daughters are going to take precedent over his sister in negotiating alliances - and he has the added problem that his dynasty is new and not going to appear too stable given recent history to any foreign power.
If Henry's sister remains with their mother in the 60s and 70s then I wouldn't rule out Edward IV betrothing her to one of his sons - with Henry Tudor in exile then the girl will be heir to her mother's vast estate and as such a catch. Given Edward IV's keenness to endow his own family on the cheap (the Warwick, Beauchamp inheritance to his brothers, the Exeter estates to his step son, Norfolk to his own son etc) there is a strong chance she will be married before Henry's victory at Bosworth.
Yes, likely if she will be of the right age can become the second wife of Richard, after Anne Mowbray's death
The King is the King and depends by enlarge who he is offering. If the child is Edmund Beaufort's say born in the mid fifties then I wouldn't rule out marriage to Dorset (the Queen,s son who in otl was betrothed to Anne Holland and after her death married Cecily Bonville) if she is daughter of either Stafford or Stanley then I wouldn't rule out Dorset or Edward,s younger son after Anne Mowbray's death.
Stanley is not going to turn down a high ranking match with what in the late 1470s was a relatively stable regime and Margaret had really good relations with Edward IV.