--Stock options are standardized contracts so it doesn't need to be the same buyer.
--Call options cannot be exercised (this would be requesting the shares) until the stock price exceeds the strike price. American options can be exercised at any time, European options can only be exercised at expiry.
--It's typically better to sell an American option rather than exercise early. Options have "intrinsic" and "extrinsic" value. The intrinsic value is what you get when you exercise. Simplifying a bit of messiness away, if your strike price is $30 and the stock is at $50 then by exercising and selling the shares you net $20. But the option at the same time will sell for more than $20. Thus by exercising early, you leave extrinsic value on the table. The time-to-expiry aspect is a significant portion of an option's extrinsic value.
Options are standardised contracts. You only have to find someone willing to sell, it doesn't have to be the original buyer. And, most options traders do not actually want to exercise the options; they simply want the cash. It is much easier to sell the contract a day or two before delivery than to come up with cash to buy the shares only to turn around and sell them again.
Yeah, but there won't be many other options to buy at this price. The idea is the squeeze, right? You buy a lot of options. You prop up the price of the underlying asset and refuse to sell. It's not a typical situation.
Genuine question, I only have very superficial understating of the option market.