Why is the exercise price of an option called a "strike price"?

I answer your first question only. The answer goes some way to dealing with your secondary questions but not with the “who?” question.

The term is simply a carrying over of a term from long established methods of conducting auctions. The agreement of transfer of goods and the price is made at the instant the auctioneer’s hammer strikes their desk.

For example, see several references to the hammer strike, of which I only quote one here, at:

“1.6 A bid shall only be deemed to be accepted by the Company at the Hammer Strike.”

United Auctions

Although in the case of financial market bargains the hammer has fallen out of use, the concept remains that the agreement to transfer ownership is made at an instant. The price is that agreed at that instant, similar to the instant of the striking of the hammer; hence the term “strike price”.