The Khajiit do not have a temple in Skyrim, or anywhere else in Tamriel.
There is a troop of Khajiit merchants that you would have to randomly encounter in the vasts of skyrim. A male khajiit guard will have a quest for you to do that involves hunting down a "moon amulet" that was taken by bandits. Get it back for him and he will offer to join you.
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The Khajiit are not native to Skyrim, and therefore do not have a formal settlement. They can be found in cities as traders or other NPC's but there is no settlement for them.
Use a Khajiit, they are good at sneaking.
Khajiit
Yes Stormcloaks are racist towards everyone who is not from Skyrim.
As far as I can tell Elsweyr had already joined with the Aldmeri Dominion even before the Great War. Weather this was forced on the Khajiit or not, the province (combined with Valenwood) became important staging grounds for the Dominion's war on the Empire. After the signing of the White-Gold Concordat both Valenwood and Elsweyr are considered to have ceded to the Dominion; and though it does seem the the Khajiit themselves are rather nuetral to it all there isnt a whole lot of information on the effect The Great War had on them. So yeah, not alot of information on it but the Khajiit are currently part of the Dominion. Hope this helped! :D
your best bet would be a male bosmer or a female/male khajiit or female argonian
You choose from the usual races, that have been in the previous games. Humans (Redguard, Imperial, Breton, Nord) Elves (Altmer, Bosmer, Dunmer) Khajiit, Argonian, Orc.
The Dragon Scale Armour, as it is expensive, hard to find, and is the best light armour, to keep you, the Khajiit, light on your feet and almost undetectable. You could, however enchant your Dragon Scale armour parts to give a boost to your sneaking and archery. I would also advise wearing a ring, not only to increase addition to effectiveness of archery, but also one handed for those close quarters attacks, or possibly magic, depending on your skills as a mage or a warrior.
J'Rasha, a Khajiit healer who can be found athis shop in Vivec's Foreign Quarter sells this spell.Source: Elder Scrolls Wiki page "Wild Open"