Kazima and Dhat al-Salasil
As is common in the Gulf, Kazima refers both to a specific place probably at the west end of Kuwait Bay and to the entire settled region around that body of water, though probably not very deeply into the deserts beyond. Excavations along the north shore of the bay suggest it was most developed during the 8th century, though of course urban development means we don't know what could have been happening along the south. It is presented in various 9th and 10th century Arabic sources as a region with respectable groundwater reserves that seems to have developed a permanent population.
The event most associated with Kazima is the Battle of Dhat al-Salasil at the beginning of the Islamic conquests in 633 CE. (A local publishing house uses the English transliteration "That al-Salasil.") However, as I argued in part of an article on Kazima in written sources published in the 2012 Proceedings of the Seminar for Arabian Studies, this event probably did not take place, and certainly was not as described.
As other historians have noted, the only source for a Battle of Dhat al-Salasil at Kazima is Sayf b. Umar al-Tamimi, whose account forms the basis of Tabari's conquest narratives. Other traditionists place a battle by that name during the life of Muhammad somewhere north of Medina, where there was a place by that name. Sayf b. Umar's work was defending a proto-Sunni position which emphasized the virtues of the Companions of the Prophet who supported the three caliphs who came before Ali. One of these Companions was Khalid b. al-Walid, the Muslim commander at Dhat al-Salasil. In his introduction to the relevant volume of the SUNY translation of Tabari's history, Khalid Blankenship noted that Sayf had moved around the dates of some battles to effectively put him in charge of as much as possible. Perhaps tellingly, his accounts still have Ardashir III as the Persian ruler during the battle, even though he died in 629.
An additional way in which this account shows Sayf's agenda is that before the battle, the people of Medina leave the army, and are replaced by a contingent under someone named al-Qa'qa' b. 'Amr al-Tamimi, who does various heroic deeds. This new commander, unknown from other sources, is from Sayf's own subgroup of Tamim. It would not be unusual for someone like Sayf to preserve an account of his own tribe's deeds which others have not, but with everyone else going on in his work is seems suspicious. Medina was an early center of support for Ali and proto-Shi'ism, and by having them leave Sayf is denying them a potential role in the miraculous success of the conquests.
As Sean Anthony has shown, Sayf almost certainly forged the version of early Islamic history which links the emergence of Shi'ism to the machinations of Jews. We probably can't prove whether anything did or did not happen at what was an admittedly strategic gateway to Mesopotamia for an army marching fom Arabia, but the account we have doesn't bear scrutiny.