Do Priests, Monks, or Nuns get married?
Generally, no, but I don't think there's any reason widows and widowers wouldn't be allowed to become priests, monks, or nuns in the RC church.
My understanding is that an RC church priest can get married, but they'd have to leave the clergy, and are still considered to be priests. I guess RC church monks and nuns can do the same - leave the clergy to get married.
Originally, priests in the RC church were allowed to get married; the church rule banning clergy from marrying was something that came along several centuries later.
I'm not a practicing Roman Catholic; I'm a non-religious individual, so I don't know how to resolve this apparent conflict that you bring up, and I have no interest in trying to explain or defend or resolve it. I'm only interested in things from the perspective of US Constitutional rights and laws pertaining to religion. I'm only interested in the these sort of basic tests for laws:
1. Does it infringe on the first clause of the 1st Amendment (i.e. separation of church and state)?
2. Does it infringe on the second clause of the 1st Amendment (free exercise of religion)?
3. Does it infringe on any other Constitutional right?
If the answer is yes to any of these questions, then the law is unconstitutional, which means the government must stop imposing or "enforcing" it on society.