Is it obligatory to inform the family members about the existence of a place thought to be impure (najis), and what is the ruling on the prayer of one who prayed in this place?

The cure for obsessive thoughts (waswas) is to ignore them and pay them no mind. As for a place whose purity is doubted, the original ruling for it is purity, and one can pray in it, because the ruling of impurity does not transfer merely by doubt.