> "Was it common to take in older people and babies? Would they have been related?" <
It was common for a non-related family to care for vulnerable people such as an orphaned child or an elderly person - as with foster children in the USA.
> "I took the names of my grandfather's parents from his Daabsattest and it shows his mothers name as Kirsten Maren Andersdatter." <
HRFFW looked at a jpg of the original, the handwritten parish register. What are you looking at? As posted earlier, Jens Mikkelsen Degn's birth is recorded in Thisted amt, in Frøslev parish. The way to find the digital version is to search the link given, and search in Frøslev churchbooks 1846-1883, then look for opslag 49.
"Now a fellow tells me that it not her first name on birth record."
Yes, re. the mother of Jens Mikkelsen Degn, he said, "Maren's death record (Frøslev opslag 168) also lists her birthplace as Elsø, her parents Anders Pedersen and Inger Marie Christensdatter, and her birth is recorded Elsø 1814-1866 opslag 45. (Note that she was born 3 July 1847, not the 2nd, and did not have a first name Kirsten as listed in the original post)."
Sometimes additional names appear in a person's records, even if those additional names were not part of their birth record. I don't know why. It's not uncommon.
> "I would like to know what exactly is the Daabsattest?" <
An online free translation program is Gramtrans at www.gramtrans.com
Record of baptism (birth/baptism were recorded together in parish registers).
> "How do I know when the info is correct?" <
heard - such as Jens Mikkelsen Degn's mother traveling to America some months before one of her sons died. The record was posted before you told us about that story.
One confusing thing is that a Danish person could use just the patronymic name (Mikkelsen) or just the additional identifier name (Degn) or both (Mikkelsen Degn). Danish women kept their birth surnames after marriage, but when they traveled to America, they did as the Americans do, and used the family surname.
"My Danish Roots" website has lots of good information about Danish genealogy.
I hope this addresses your questions.