You can. But that still doesn't tell you if you've had COVID. Antibodies wane overtime and you can also test positive for antibodies after having had a vaccine. So even if you have been taking antibody tests every couple of weeks year now, you could have contracted it before the tests were available (it was about a year before they were publicly available in much of the US), or after a vaccination.
Depends on the test. The right test can tell the difference between the set of vaccine antibodies and the set from an actual infection. Vaccine only creates antibodies that target the spike protein structure. I participated in a study and got updates every six months.