Those are easy to understand but hard to explain. this requires you to know what is what. For ex, she has appointed her secretary personnel manager. This means she’s the director and promote here can be understood like give someone a higher position than he has now in the company.
1.a. She has appointed another woman to be assistant personnel manager.
1.b. She has appointed her own assistant personnel manager (maybe to another position).
2.a. My lawyer gives free advice to the poorest people.
2.b. My lawyer gives free advice that is the worst (poorest) possible.
3.a. I will say that you are my secretary.
3.b. I will call my secretary for you.