I have questions for people who know these rankings, let's focus on NET for now, better than I do:
I know less specifically about NET but more about computer rankings in general and will take a crack at this.
1) Once the OOC is over, is there effectively a set amount of ranking capital to go around between the members of each conference, or can the efficiency stats change that significantly?
Generally yes. Once all of the OOC games are complete the average ranking of the conference is basically set and then the teams will just move around relative to that average.
As an extreme example, if there are three teams in a conference, and they comprise the top 3 in the NET as of the beginning of conference play, is there anything that can happen in conference play that could knock one of them out of the top 3? How about two of them out of the top 3? How far could they fall, realistically?
Depends what you mean by realistically. If they just lose to each other and beat the other teams in their conference they will likely stay very high. But if they finished at the bottom of their conference they could certainly fall quite a long ways. These falls would be offset by gains for the other teams in the conference such that the overall strength of the conference remains the same.
2) In conference play, it seems like we should effectively be rooting for the teams we play twice to beat the teams we play once, regardless of our performance against each. True?
True.
3) Later in the season, should we be rooting for the teams we beat twice (knock on wood that there will be a couple) to beat the teams against whom we went 1-1, who we should be rooting for over teams that swept us? I suppose it depends more on whether the game has the potential to knock one of them into a different quadrant, but if that's not the case, should we be rooting for, e.g., PSU over Illinois later in the year? Indiana over MSU now? Or, within a quadrant, is the betterment of an existing win fully offset by the deterioration in an existing loss in that case?
I don't think there is one answer to this, it depends on specific situations and how specific ranking systems work. It also depends on how good YOUR team is. For example, consider two different schedules:
Schedule A:
vs #2 team
vs #300 team
Schedule B:
vs #150 team
vs #151 team
which schedule is tougher? It actually depends on how good you are.
If you are the #1 team, for example, schedule A is clearly harder. You have ~ no chance of losing to #150, #151, or #300, so the only thing that makes a schedule hard is playing other top teams.
If you are the #320 team, however, schedule A is clearly EASIER. You have ~ no chance of beating #2, #150, or #151 and so the only thing that makes a schedule "easy" is a chance to play other bad teams.
If you are the #149 team, the schedule are of approximately equal difficulty, but there is a lot more variance in schedule B (where you are expected to go 1-1, but any outcome is plausible) vs schedule A (where you basically always go 1-1).
In general, I think it is PROBABLY better for us to have some top teams on the schedule and some worse ones rather than to have the whole Big Ten clustered at good but not great, so I would think we should root for the better team in any matchup between teams we've played the same number of times. But this effect is small and I might not even be right about that, it's very complicated.