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Of course they did.

There were two things that united the Greek city states: Common language, and common religion. The Spartans believed in the same Pantheon of Olympus as the other Greek peoples. Each city, of course, had it's own special gods; but the pantheon was more or less universal throughout the Greek world.

The Greek Religion was essentially Animistic. The forces of nature were each controlled by a seperate god whose intercession could be obtained through sacrifices. The Greek religion did not emphasize the importance of spirts and the supernatural. Indeed, many Greeks did not believe in an afterlife at all.

Yes, they did. They used a slightly different dialect than Athenians, but it was Greek nonetheless. However, Spartans did not pay too much attention to intellectual pursuits and didn't produce any great literary works (that we know of). Our primary sources on Spartan history and culture are actually not Spartan. Xenophon, for instance, was an Athenian who simply admired the Spartan system. Most examples of Spartan writing we have come from inscriptions, not from any form of literature.

Yes, dorian dialect of Greek.

Ever wondered why the noun is mAchIne and the adjective is mEchAnical? It's because the Romans took the noun into latin from the Doric greeks of south-east Italy. The adjective comes from the Attic Greek form

Yes. Greek...