There is very well-documented history of the Hoppers family. Hoppers is pretty much how the name was spelled in North Carolina by the late 1800s. You will also see Hoppus, Happes, Hoppes, Hopperas, and Hoppas. In Germany it is Happes and we still have many cousins living there.
A couple people I know of have done extensive research on the family, including going back to Germany. The family came here about 1750 (there is an exact date), landing in Pennsylvania. Two brothers, Georg and Michael, were indentured servants in Pennsylvania for several years. Michael eventually went north and served in the Revolution. Georg (our line) went to North Carolina.
The early Happes family in NC seemed fairly ambitious and involved in the church and community. Jacob was born around 1802-1803 and was the youngest of 9 children. His parents were John Daniel Hoppes and Anna Mary Fender.
You will see that Daniel Hoppes owned a ton of land in Alleghany County and surrounding areas and was friends with some Moravian bishops who travelled the area doinf missionary work. There is also documentation in Moravian records that Daniel's father Georg (the immigrant) hosted Moravian clergy at his home on many occasions. I seem to recall reading somewhere that Daniel was a Methodist but did not have access to Methodist chuches and clergy and so became friends with the Moravians.
I'm not aware of any picture of Jacob. He was a farmer according to the census. We do have pictures of two of his children with his wife, Kiziah Landreth. He and Kizzie had 8-9 children.
I can't say that Caroline was not born in England because I don't know.