This can be stated in active form. Possible meanings are 1) David put the crown on his own head or 2) David's men placed the crown on his head. (See: [[rc://en/ta/man/translate/figs-activepassive]])
These two occurrences of "he" refer to David, but they also refer to David's soldiers who helped David do these things. (See: [[rc://en/ta/man/translate/figs-synecdoche]])