Some great questions and ones posed by many often. Without trying to find the posts to direct you to, I will just try to answer them from what I know/recall.
Yes, the Fan Survey can give you some visual info on the PR's effectiveness. But I don't hold this as 100% accurate. Rather, a good guide.
"Three times per week following games" means exactly that. On the day after a game (not sure of the exact timing) a survey is taken. I wouldn't read too much into how the timing of this survey affects anything. And, if you are knocked out of the CUP, they refer to the scrimmages most teams have in place of a cup game. That is, most teams place 2 league games and 1 CUP game (Scrimmages once they are no longer in the CUP). these are the 3 games they refer to.
What does it mean ..."at the beginning of each game?" Well, every game played on BB is a simulation run prior to actually being available to view through the viewer. Therefore, the beginning of the game no doubt refers to the period of time (15 minutes?) that the simulation is running and 'creating' the game we can then see "live" in the viewer at your country's designated starting time. That is, we never actually see any game "live" ever...as they have already been run and then made available. So, the "beginning of the game" would refer to that small amount of time (I believe about 15 minutes) before we can actually see the game "live" in the viewer.
So, yes, if you buy a higher level PR guy or Doctor at least 15 minutes before a game starts on the viewer, they are factored into that particular game. For example, if you are in a Final (3 game series) and you have Home Court Advantage (HCA) and have a Crowd Involvement (CI) PR guy, you will get a small boost in that first game and last game (if it goes to 3 games) assuming you don't fire the guy before the 3rd game. This also means that if you were to keep your CI PR guy for game 1 (and get the small boost), you can fire and then hire a National Appeal (NP) PR guy for Game 2 of the series to give your team a little boost in that away game. Then, of course, you would then fire him and rehire a CI PR guy for your Game 3 if needed. Tens of Season ago I used to use this method successfully. Obviously, this strategy would only work if you have extra cash to burn and really want that promotion.
I hope this example gives you an idea of how the PR guy works.
The Doctors, however, can work "after" injuries. The PR guy doesn't work in the same way but can, as I noted above, if hired and rehired before the next game, be used for small increases in a given game.
Hope this makes sense. I'm writing it on the fly...
Home Grown; for teams who like a challenge!