Married priests are becoming more common in the Catholic church, particularly as the number of young men entering the priesthood is declining. The rule is simple - if you are married and wish to become a priest, no problem, and this is common among Anglican clergy who have converted to Catholicism. If however, you are a priest, then you are unable to marry after your ordination.
I doubt that anyone other than an Anglican priest (or probably an Orthodox one) could become a Catholic priest if they were already married today, but certainly before c 1000 AD, it was common for priests to be married.
They have. Technically they are not allowed connubial relations after ordination, but I dont think anyone is looking. Actually priests have a long history of live-in lovers. King John famously introduced a "sin-rent" on clergy with, umm, companions, which was a major source of income.
That said, under the Pauline priviledge a married man who becomes a priest can be divorced under church law. His "marriage " to the church overrides that to his wife.
Sorry incitatus but the Pauline privilage relates to a husband or wife who's partner is not a Christian. In order to divorce into holy orders both partners must go into a monastic house (like Abelard and Heloise).