I have gathered my thoughts a little more about Demont Morenzy. Sorry but this will be a long message.
I am doing this research for an ancester of Demont who lives in Pennsylvania.
Demont went to USA in 1848 as on the 1900 USA census
He was born on 20 May 1832 in Durham as on the 1870 USA census
He quaified as a doctor in 1854 from the Philadelphia college of medicine
He married Catherine Rebecca Carpenter in 1855
He says during a court appearance as a witness that he visited England in late 1858 then went to Belfast and worked as doctor there for one year and then went to Liverpool for 6 weeks, not working, then worked on passenger ships as a surgeon for 2 years.
He had 4 sons, one died in infancy and after his wife died in 1876 he moved to Illinois and remarried and had 2 daughters. he died in 1905.
I have drawn up a family tree from your message and ruled out the first two Williams as beig too old or dead to be his father and William 111 who died in 1850 can't be his father either as who was Demont visiting in 1858?
The William 1V is too young to be his father.
Demont also stated that his uncle worked as a visitng physician in the Belfast hospital in 1859.
Who were the Durham relatives??? ..this seems a likely avenue of research.
What school might he have attended in England???
I hope you can answer some of this puzzle...