While this is for practical purposes true _now_, there actually were a small number of married popes (https://en.wikipedia.org/wiki/List_of_sexually_active_popes#...), and there have been a few popes who were not priests before being elected (if you want to be pedantic, Peter wasn't a priest, and may have been married, but there were later examples).

> all adult Catholics can become Pope

All adult male Catholics, though also see Pope Joan (probably didn't actually exist, but was generally believed to have existed until quite recently). There's also no actual age requirement, though in practice the youngest pope was _probably_ 18.