I don't know much about contract law, but it may be interesting to know that a resting order on exchange, with a set price and size, is called a quote.
The terminology offer is used in financial markets for a resting order to sell, distinguishing it from a bid which is a resting order to buy, although many market participants will actually use the terms bid and ask rather than bid and offer. Whether this is to avoid confusion with the contract law term, I have no idea.
It won't surprise you to learn that I also think that your perspective #2 is unworkable in a situation where you have multiple exchanges (how would it work - would you require that quotes on exchange B must remain for a specified period after a quote on exchange A is hit? That doesn't seem sensible).