Yes. Options can be sold without you owning them but this is not known as short selling. When you buy an option, you pay out money to someone and obtain the right to buy (or sell, in the case of put options) the underlying at the strike price. The seller of the option sells you this right to buy (or sell) the underlying at the strike price and in return for a premium. The seller therefore takes money in, but also takes on the obligations that go along with the contract.

As soon as you tell your broker you would like to exercise your right to buy the futures contract you are deemed to be a contract owner. Because of the irrevocable nature of the call exercise, you will be buying the futures contract at the strike price, and you can sell those contracts immediately after giving instructions to exercise.

Options will not move as much as their underlying unless they are in-the-money and/or very close to expiration. The amount an option can be expected to move given a 1-point move in the underlying futures contract is called delta.

No, because the value of the Option will depreciate with time and is worth nothing once expired.

Options is both an exchange traded product and an OTC product.

Writing an option provides one with an additional source of income arising from the premium one receives from the buyer of the option. The premium also serves as a cushion against the risk exposure one would incur.