Yes, the Rundfunkbeitrag is per household. There are ways to get a reduction, but only because of financial difficulties or a handicap. The devices you own have no effect on the TV tax. It has been so for many years.

https://allaboutberlin.com/guides/gez-rundfunkbeitrag

Yes, you have to pay the Rundfunkgebühr also if you don't have a TV but your computer has access to the Internet because public broadcasters also have a presence on the Internet.