I agree. If it requires a body, then there shouldn't be a body to tag. While we have no reason to believe that she won't return at the reset, there is always a first. And I've heard rumors from the other campus that people have died and stayed dead there. Whether that's true is another story.
No, they didn't become monoliths. The monoliths broke through later after Carter's destruction. It tried to get through once, but couldn't. Michael said the monolith, or the entity behind the monolith, exploited the nanosecond at the reset to break through. It would take months for that to happen.