I think this the part I struggle the most with. What effect do these have? I mean I don't even know how to estimate what the impact might be. What do they effect exactly? Public opinion, more than that?

Yes, they have subtle effects on public opinion (the three approval metrics: popularity, press approval and authorities approval). Some wordings may be more suitable than other, depending on which of these three stakeholders you want to appeal to. For example, choosing to reveal more about your internal process might look good to the press, but won't be seen as a good thing by your bosses.