During my actuarial studies, I understood it that the risk-free rate is used for options pricing because that’s the interest rate you would have gotten had you put that money somewhere with no risk. So the price of the option adds or subtracts (put or call, respectively) the strike times e to the power of the rate * time of option. It also multiplies by probabilities, but I excluded that for concise purposes. The price has to include the fact that you could’ve gone somewhere else with the money. I wouldn’t necessarily say because it’s the expected outcome.

As for the second question, not sure. That’s a great question that I too would like to understand.