Yes, as you say, the Jensen children in 1834 should have a father named Jens. I'll let another volunteer help with that question. The next earlier census before 1834 is 1801.
If you visit ddd.dda.dk, an easier site to use, look for the little flags to the right and choose the British flag for "English." To get the 1870 record, below, choose Census / Search for Individuals /autocheck of database /county "Soro," /district "Alsted," /parish "Alsted" /Christen Andersen.
Sorø, Alsted, Alsted, alsted, , en gaard, 10, FT-1870 [en gaard = "a farm"]
Christen Andersen 24 Gift husfader gaardmand Alsted
Karen Andersen 28 Gift husmoder Alsted
Anders Jørgensen 6 Ugift barn Alsted
Jørgen Cristen Andersen 3 Ugift barn Alsted
Hans Christen Andersen 1 Ugift barn Alsted
Sidse Andersen 63 Enke slægtning Alsted
+ 5 tjenestefolk (laboring folk)
The family seems to be using "Andersen" as a surname in the updated naming mode. Some families of this era were still using patronymics.
Gift = married, ugift = unmarried. Barn = child, i.e., their child. Enke = widow. Norman Madsen's Danish English Dictionary online helps with old job titles. Use % as a wildcard to replace letters that might throw off your search at DDD (e.g., Christen/Kristen).