Short answers, pulled from the story.
The Geatish Society (Götiska Förbundet) was founded in 1811 by a group of Swedish poets and authors as a literary club. Its purpose was to raise the moral tone of society by studying Scandinavian antiquity and reviving interest in Norse mythology and Viking culture.
The Society published a magazine called Iduna, which printed poetry, essays, and commentary on old Icelandic literature and history. Its editors included the celebrated poets Esaias Tegnér and Erik Gustaf Geijer.
Esaias Tegnér's epic verse Frithiofs saga and his shorter poem Skidbladner were composed under the Society's influence, as were Erik Gustaf Geijer's poems Vikingen and Odalbonden. All were at least partly published in the Society's magazine Iduna.
No. The myth that Vikings wore horned helmets originates with the Geatish Society, whose members occasionally wore such helmets at meetings. There is no evidence that actual Vikings ever wore them.
The Society was formally dissolved in 1844, following the death of Jakob Adlerbeth, after having been dormant for more than ten years. Its library and archive were given to the library of the Royal Swedish Academy of Letters, History and Antiquities (Vitterhetsakademiens bibliotek), where they are held in the special collections.
The Society's Norse mythology and imagery became popular in the German Empire through comparable organizations in the Völkisch movement, and similar themes were later taken up in Nazi Germany. Viking imagery appealed to those movements because it evoked conceptions of Germanic peoples unaltered by outside cultural influence, and associated them with a warrior ideal that proved adaptable to pan-Germanic and Nazi ideological purposes.