3 it is highlighted the difference between no arbitrage and settlement pricing of the options
and something else.
This ("and something else") is a classic
Something is related to my point on options pricing, which interprets premium as settlement between buyers and sellers and therefore implies market risk of the premium. Nonstochastic BS premium is implied by oversimplified problem setting that follows from no arbitrage framework of the pricing problem. It will be o'k if we had sufficient conditions that convince us that buyers and sellers always follow the pricing rule which is directed by BS hedged portfolio.
In particular, when we interpret price as a solution of equality of EPVs of two cash flows buyer and seller like irs we interpret price as an estimate of settlement price. It looks much better for me than interpret swap price like a portfolio options in BS world.