As Spartan has said, there needs to be a formal resolution to exclude the public in accordance with the provisions of the Public Bodies (Admission to Meetings) Act and the reason for the exclusion needs to be identified. Generally, embarrassment is not a valid reason but a discussion on staff related matters such as disciplinary matters or salary discussions would be a valid reason. In the scenarios you've identified, I'd question the council's power to act for no. 1 in accordance with the Ledbury case. 2 might be valid (difficult to say without knowing more about the relationship. 3 is often, but not always taken in private session on the grounds of being commercially sensitive and I'd argue 4 would definitely not meet the criteria for being in private session. You also need to remember that whilst the discussion can be confidential, the decisions cannot. Formal meetings at which decisions are taken must be held in public.