1. There are no notes of him being married.
2. There are no notes of him having children. Even less that his possible children would have been masters/goldsmiths.
3. Yes there are records. His last years he lived in poverty and died 1868. Hes last work is dated 1835 and the workshop was closed down in 1837.
4. Even if his possible wife or children would have continued the business they are neither mentioned nor listed in any source....their names are unknown!
A little research could clear things up:
At the census 1865 in Bergen, Norway, there were two persons by the name Jacob B(eier) Hagelin, both goldsmiths.
The oldest was born about 1792, and died June 9, 1868, 78 years old, widower
. (Death record: Parish record Bergen, Domkirken 1863-1876, page 44)
The young one, Jacob Beier Hagelin, was the son of the old one
. He was born on April 1830 in Bergen as son of goldsmith Jacob Beier Hagelin
and wife Gjertrud Bergitte Boland
. (Baptism record: Parish record Bergen, Korskirken 1823-1835, page 102)
I have added the sources for this information, in case someone wanted to check the records. So in this case:
1. Yes, he was married
2. Yes, he had at least one son
4. The name of his wife and his son is registerd in the parish records for Bergen.