Is the inheritance, after being divided and each heir's share allocated, considered private property for him, and is it permissible for him to dispose of it by placing a lock on its door to protect his belongings and privacy, especially if his share represents an entrance to the parts of other heirs, and one of them had asked him not to place his belongings in his share?

This division is effective and binding. You must allow your siblings to pass through the pathway located in your share. If a private path was not stipulated for each share in the original division, then the path remains shared. The owner of the door has the right to dispose of it without preventing others from passing, and you are not permitted to benefit from their share except with their permission.