AC-120-12A helps define private vs common carriage further.
Your examples.
1. With your friend - no problem
2. Different friend- Depends on how much they pay. There might be some issues if you made repeat trips, because the "original" friend could be considered an agent for your operation.
3. Business man- still legal as long as you know him personally and with having him rent a plane doesn't matter because he is furnishing it.
4. Boxes- Depends. Because if the boxes are from the general public, then he is acting as the avertising agent. Otherwise, if it is just to ship parts to supply his business; no problem.
5. Two friends- yep it's basically corporate.
Think of common carriage as are you holding out to the general public. Flights with friends as a common connection is fine.
The best catch all answer to give your answer to the DPE is "if I have questionable scenarios, I will contact the Regional counsel of the FAA before engaging in the activities."
However, you should be able to answer some basic examples.