An even older 'rap' was 'Rap-a-tap-tap'.

portion and fortune would have been almost interchangeable.

Yes, portion is a dowry, what she would receive as a marriage dowry from a relatively wealthy family such as a landed farmer. It's 'portion' in the sense that in those times people had large families and each child would expect a portion and would usually have a good idea how much it would be. A common phrase in the ballads 'you will not get one penny portion'

They would demand it if it had been promised and it was seen as a right, but if she didn't marry someone of her station or higher, the father could withdraw it. Fortune would more usually refer to the inheritance at death of a parent, and this would have been willed so in some ballads if the father has died and left her say £10,000 in the will there was nothing the mother could do about it even if she married the servant.