The place is Linnau, today part of Nordhackstedt in the German state of Schleswig-Holstein as you know already
Yes, that was a home for poor people. The whole family lived there:
Johann P. Johannsen, 40 years, married resident
... Johannsen, 38, married resident, his wife
(It would be very unusual to list the wife's maiden name on such a list. So I think her prename was shortened and the last name was Johannsen)
then follow the unmarried children.
I saw todays's posts on the Danish board, a great help. I suggest you write to the archiv as suggested.