We often use 'themselves' instead of him or herself, as the latter is very clunky and awkward. As people are talking about gender-free issues, too, there is a move toward using 'them/themselves instead of him or her as well, although it might not be strictly speaking grammatically correct

Yes, as long as it's plural

Themself for singular. Themselves for plural. Themself is newer and gender-free. It's very commonly used.