Only the first point “Good and evil are objectively real” is a necessary part of moral realism. Sometimes the first half of the third (“We have an objective moral obligation to do good and not do evil”) is included, but by some definitions that is included in what good and evil mean.
All the rest are assumptions that many people who believe in moral realism also happen to hold, but aren’t part of moral realism itself.
Only the first point “Good and evil are objectively real” is a necessary part of moral realism. Sometimes the first half of the third (“We have an objective moral obligation to do good and not do evil”) is included, but by some definitions that is included in what good and evil mean.
All the rest are assumptions that many people who believe in moral realism also happen to hold, but aren’t part of moral realism itself.