Short answers, pulled from the story.
The name Geat derives from the Proto-Germanic word geutaną which means to pour. Ancient scholars suggest the name might refer to the river Göta älv in modern Sweden or people who live near a specific stream like Trollhättan Falls.
Ptolemy wrote about these people in the second century AD under the name Goutai. Jordanes described them as Gautigoths in the sixth century alongside Ostrogoths and Procopius referred to them as Gautoi during that same era.
The Geats divided their land into several petty districts each with its own popular assembly called things. The Thing of all Geats occurred annually near Skara within Västergötland while Östergötland held an equivalent gathering known as Lionga thing.
Jordanes wrote that Goths came originally to Dacia from the island of Scandza and described three tribes on this island called Gautigoths Ostrogoths and Vagoths. This implies the Geats were Goths rather than vice versa according to his account.
Until 1973 the official title of Swedish kings included King of Sweden the Geats and Wends. Carl XVI Gustaf decided alone that his royal title should simply be King of Sweden marking a final step in national unification.