Yes, you <Draw 1> if you choose to not return a card from your trash to the hand.

Yes, you gain <Draw 1>.

It can be activated after activating the used Option card's [Main] effect and trashing that card.

No, it doesn't trigger. If an Option card's effect activates without using it, such as activation by a [Security] effect or <Delay>, the "when you use an Option card" effect doesn't trigger.