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Yes. They're usually a mixture of sand, oil, clay, and local magic. They are not grass. Although some greens occasionally feature bonus weeds or rogue patches of grass, thoughtfully included to increase the degree of difficulty.
Technically yes. Around Saskatchewan, however, "dirt golf" is often the term people use, and we're not about to argue with local tradition. That's why you'll see the terms sand greens and dirt greens used interchangeably throughout this site.
There should be a handcrafted and highly engineered rake available for you to smooth the green once you're done putting. As the old saying goes: loser rakes the green.
Because golf was supposed to be fun before it became a mortgage payment.
Probably. Check with the course, but nobody has ever won the Masters in a bunny hug either.