I have been looking at the Stockton sheets of the 1881 census and whilst I haven't found anything to answer any of your questions, it is interesting how the entries paint a picture of the background in which the family was living in Sheraton Street, Stockton.
I see that also in the household was Mary A Thomas, 20, Domestic Servant unemployed, who was born in Dowlais, so it is possible that she is a relative or a family friend, bearing in mind that Ann was born in Dowlais. I also see that of the children, Elizabeth, Thomas and Eleanor were born in Rhymney, so presumably that is where the family was living before they moved north.
Interestingly, next-door to them in Sheraton Street, Stockton, is an Elizabeth Williams, aged 32, who was also born in Rhymney, and further along the street there are quite a few Breconshire families. In addition there is the O'Hara family from Ireland whose son, Stephen O'Hara, was born in New York. As the majority of the men were employed at the ironworks (by the look of their occupations on the census) it is likely that they all knew each other, so who knows what stories the O'Haras, and other travelled families, had to tell? It is not hard to imagine why someone would want to leave such an area to seek their fortunes abroad.