It has been said that there is some likelihood that exposure to a previous Coronavirus made some people partially resistant to Covid-19. Would that mean that there is a chance that some people test positive for Covid-19 antibodies due to a different strain of Coronavirus?
I don't think so. Antibodies are pretty specific. However it's possible and there is some data to suggest that some people have T-Cell level immunity to SARS-Cov-2 that was likely induced by exposure to an earlier coronavirus.
Not always. Famously, cowpox antibodies protect against smallpox.