My recollection from reading years ago is that priests weren’t allowed to marry because in ancient times they would establish churches in remote places that might rarely be visited by church authorities. If the priests married then the churches might be claimed by heirs as their property and the church would lose it. (Dons protective clothing and hunkers down.)
Your recollection is indicative of poor knowledge of the topic.
No. Closer to the fact that care for his personal family might compete with care for his flock. I suppose it’s plausible that a given priest might have tried to set up some legal situation where his family might inherit what the church might have, but a church building? Not seeing how he’d’ve been able to have his children inherit a church building anyway. The very practice of holding a mass there would pretty much establish it as belonging to the Church.