True that dust clings to a fan shroud, but you have to consider all the factors, static, oil in the air, moisture in the air, etc. it’s hard to say that this is conclusive evidence of mask effectiveness.

Besides that, a fan is a 1-way movement of air, many fans have a self clean mode that actually works fairly well (it spins in reverse). So in effect, by normal breathing, you are diminishing that effect of static cling filtration. Additionally, the static cling effect could actually worsen it, because now you have a larger surface area to suck through, and less chances for it to escape.

Sickness can be made worse by being social, but generally it depends on each person and how they are wired. If staying home makes you feel sad and depressed (especially if alone), you’re health is less likely to improve, whereas if you enjoy solitude, it would probably help you to avoid people.