It is generally considered proper to button the middle button of a three-button blazer, and to leave the bottom button unbuttoned. For a two-button blazer, it is customary to button the top button only.
Yes, it is customary to unbutton your suit jacket when sitting down. Leaving the jacket buttoned while seated can lead to unsightly creases and restrict your range of motion. However, if you are wearing a waistcoat or vest, it is typically left buttoned, as it is designed to provide a structured look even when sitting.
