Do I have to click the ads to receive BAT?
No, you definitely don't. You receive BAT just for seeing the notification appear on your screen.
Opening the ad, interacting with the site, or spending time on the site does not reward you any BAT and does not change how change how much BAT you receive.
In future Brave may introduce ways in which ads require interaction, but there has been no official announcement of how it would work, or when it would happen. [Current August 12 2021]