The expectation is that PCR negative is roughly correlated with fighting off the disease in the short term, and basically perfectly correlated in the long term.
Antibody tests only work after several days of infection, but some of them are not very specific to SARS-CoV2 and therefore have a high false positive rate.
So you really need use both tests, but you can't just OR the results together, because then a faulty antibody test will massively skew the results upward.
No, it only works if there is enough virus to be detected. If you are infected, you will have a high enough count to be detected. Each type of PCR test is highly selective. The point of them is that they can differentiate between many types of virus, depending on how its setup.
> Antibody tests only work after several days of infection
Yes. Depending on the type of test, and how its done. it can be up to a month before these tests are accurate.
This is the reason why China started to accept clinical diagnosis like chest scans, causing a sudden big spike in cases.
Even after the viral load in the upper respiratory tract drops off, there's still lots of virus around. You'll likely test positive -1/+2 weeks around onset of symptoms.