[Sebastiano]

Originally Posted by janaf

1) If the regular member OP does not set a PT post as private, the admin sets the message private, then can the OP make the messge public again? Othterwise, can this be prevented somehow?

You can control each user group ability to change the private setting after creation with the PT permission Issue Editing Permissions -> Can Edit Private Setting After Creation.
By default, registered users don't have this.

Originally Posted by janaf

2) If OP sets the project as private, can the admin make the project public?

By "project" I think you meant "issue"? If this is the case, the answer is still the permission mentioned above: Issue Editing Permissions -> Can Edit Private Setting After Creation.
By default, admins have this.