1. Well the thing is that they had shabbos guests the shabbos after purim, who came down with covid like 2 days later. That was before they (the hosts) got so paranoid. So it's possible that they caught it and were asymptomatic (I don't know how likely, but possible.)
2. I don't know but it might help. But whenever someone mentions to them that maybe they should get tested, the answer is that they don't want to leave the house
3. They are elderly and may have risk factors, I don't know
Is staying home causing them to forgo needed medical care? To eat poorly? Risk losing a job? Or causing
them distress?
If not, their choice to stay home may be rational, not necessarily paranoid, since being elderly is a risk factor. Our perception of the passage of time also seems to change as we age, and the prospect of waiting a few more weeks - or months - for greater clarity in the situation may not faze them as much as it would a younger person.
If
they want the test, check your county health department. We have something called "homebound testing", for elderly, disabled, those without transportation, but I think at this point that might be limited to testing for the virus, not the antibody.
