The presence and severity of symptoms varies for COVID just like it does for literally every infectious disease, for everything from colds and the flu to plague to ebola to polio to HIV/AIDS. We can detect COVID infections with a variety of different COVID tests - claiming otherwise is wrong. Diagnoses can also be made through differential diagnosis of symptoms.
Yes. Determining Covid-19 is a diagnosis.
Determining presence of SARS-CoV-2 does not test for Covid-19 but does support the diagnosis.