"Illustreret Nyhedsblad" translates as "Illustrated News"; it was a weekly newspaper. The contributors included Ibsen, Bjørnson, and Collett - heavy names in Norwegian literature.

The footnotes read:

First image, one star: A later-deceased Danish mathematician.
Two stars: [Niels Henrik] Abel had, before leaving, written a short paper on this issue, in French; but to lessen printing costs he had shortened it to a half sheet [of paper], forcing him to leave out many intermediate results and making it hard to understand. The [German] mathematician Gauss therefore said, upon seeing the result, that he would himself prove the possibility of the solution [?], but later admitted that Abel was right.

The paper has 'Gøttingske' where I have translated 'German'; this seems to be a mistake on their part, since Gauss was born in Braunschweig, but attended the University of Göttingen. (Either way, 'famous' or 'world-renowned' would be better adjectives - some patriotic bias there, possibly.) The word I have translated as 'solution' is 'Opløsning', which in modern Norwegian means a chemical solution, but in context seems to imply a reduction or a division into parts. Possibly it refers to the problem of finding a closed-form solution for arbitrary fifth-degree polynomials; Abel's best-known result was the proof that this cannot be done with only the four arithmetic operations and roots.

Second image, one star: Presumably the same [one] who is mentioned in Humboldt's letters as a collaborator in Kreuzzeitung's gossip section.
Two stars: A Jutish [?] student said of him, in this connection: [Whited out]
Three stars: At that time he was an assistant at the observatory in Altona; he is currently employed by the observatory in Dorpat.

Kreizzeitung seems to be a proper name, probably of a newspaper; the word I have rendered 'gossip section' is 'feuilleton' - I have guessed that it is used in its original French meaning here, but there are some others. In modern (or rather, middle-twentieth-century; I don't think you would see the word used much today) Norwegian it would be spelled 'føljetong' and mean a serial, most likely of fiction.