Virginity is not a requirement. It’s a matter of celibacy after one takes vows. One of our priests wash’t ordained until he was in his thirties, before that he had come to the US from Ireland (illegally) and had worked construction and lived a conventional single man’s life in Northern California, including dating women and having a long term girlfriend for a while.

And it is not uncommon for widowers to join the priesthood after losing a spouse.

No. Some priests are even widowers. Source

I think the Catholic church is in need of nuns and priests since most people don’t want to live that kind of a life now, and so I would think (and hope) they’d be grateful to have someone willing to give up sex and money for a life like a priest or nun lives. Yes they get housing but a lot is expected of them in return.

No. I saw an article years ago about a man who had been married with children who became a priest later in life.

No.

No, but they do have to like children.
There was a young chaplain from King’s, Who talked about God and such things, But his real desire, Was a boy in the choir, With a bottom like jelly on springs.

Our priest is a widow with grandchildren. Some priests transfer from the Episcopalian denomination and they have wives and children.