'Sine qua non,' you might hear in intellectual circles, academics, or certain podcasts. But it would be very unlikely to hear it in any kind of normal situation.
We say 'in the cards,' somewhat regularly in the US, but I've never heard 'on the cards.' You can hear the negative version, maybe, even more often. Like if something didn't work out for me, I could say 'Ah, that's okay, it just wasn't in the cards.' It speaks to luck or fate.
'Bore the pants off someone' is still somewhat used, but it sounds kind of antiquated. Like it was probably more popular in the 90's. Although if you're in a workplace or amongst people ages 40-60 in the US, it'd be understood by most people.