I think you have that backwards.

False negative seems extremely plausible. If you're sick, but your viral load is low, it should be possible to collect a sample without a virus particle. If the sample doesn't contain a viral particle, it will necessarily come back negative.

False positive seems unlikely, as you'd have to have something that survives several cloning cycles that ends up looking exactly like the markers you're matching against.

It's the opposite. The PCR tests are more specific (99%) than sensitive (perhaps 90%, we're not really sure).

30% chance of false negative which is why they do 2 days in a row, which bring it down to 9% chance of false negatives.

It’s the opposite. False positives are highly improbable. False negatives happen more regularly.

If there are very little viruses, and the swab/sample didn’t contain any you would get a false negative test.