1. Yes, exactly.
2. No, you can never lower that number. AIP is completely unrelated to this number (positive or negative). The number of reinforcement points are based on the number of planets the AI does not control, and it caps out around 12 or 15, something like that (per AI player, as with everything reinforcement or wave related). A bit different based on various sizes of maps. The AI is granted these number of reinforcement points every x amount of time, where x varies close to linearly by difficulty level (so the harder the difficulty, the more frequently the AI gets a pool of reinforcement points to spend, same as it gets waves more frequently). Unlike waves, there's not a random time component in the reinforcement point distribution, to my recollection. Or at least not as much of one.
Reinforcements are two-factor, which I think is the source of most of your confusion: there are overall reinforcement points, which are at the galactic level. You can't alter these in any way, aside from giving the AI more as you destroy its command stations. But that's literally your only interaction with it. However, all those points say is "do a reinforcement event at a planet," and the AI can choose which planets. It can also choose to spend two points on one planet during one reinforcement cycle, or in rare cases (mostly home planets) up three points on one planet. All of this is just the first of the two factors.
3. This is where the second factor starts coming in: what does a reinforcement event at a planet "translate" into in terms of ships? Remember, there are between 0-3 reinforcement events per planet in the cycle, depending on where the AI decides to allocate its points. Anyway, how a reinforcement event happens on a specific planet is enormously complex and is affected by AIP, number of guard posts at the planet, if there is a command station at the planet, and so on. So: if you kill any guard posts at a planet, wormhole or otherwise, you substantially reduce the effectiveness of reinforcement events at that planet only. There is no way for you to adjust this directly on a galactic level, with guard posts or otherwise.
However, indirectly, you can affect the galactic reinforcements by removing all the guard posts at valuable planets, and then keeping those planets below their planetary ship caps. The AI determines which planets to reinforce at while being blind to how many guard posts it actually has at that planet. It knows only if it can reinforce there at all (based on having any reinforce warp gate ability units, and based on having available ship cap), and if it makes sense to the galactic strategy to do so.
That might sound complex, but the strategy in question is simple: if there's a high alert planet that is near your planets and the AI spends a reinforcement point there out of its limited pool, you can control how many ships it gets based on how many guard posts it has there. If there are a dozen guard posts, then the AI just got a ton of ships. If there's next to none, then it got a fraction of that. If it's just the command station and the wormhole guard posts, then it got close to comparably nothing, and in return it lost a reinforcement point that it could have spent elsewhere. The key thing here is that if you'd killed the command station and the last guard posts, or if you let the AI planet sit there at ship cap for that planet, then the AI will not be able to reinforce there and so will have no choice but to spend its reinforcement points elsewhere, which actually is probably to the benefit of the AI since that means it gets more overall ships somewhere.
Another strategy that people use is alerting a bunch of planets in a part of the galaxy they never have any intention of going to. That causes the AI to burn tons of reinforcement points in a useless area trying to defend against something you're never planning on actually following through on in the first place. That's much easier and more effective as a way to alter the tides of galactic reinforcements.
4. So, per the above, no this has no effect on galactic reinforcements -- except to improve it. By firstly giving the AI another reinforcement point if it's not already at cap on its reinforcement points, and secondly by making the AI spend its existing reinforcement points somewhere else.
It's kind of like water pressure in a hose: if there are 90 planets that the AI can reinforce into, then you have a loooooong time before you start seeing substantial buildup except on the planets you have on alert. If you've alerted 90 planets, then each of those are also going to be filling up super slowly. But if you've alerted 1 planet only, that one is always going to be an incredibly beast to deal with because both AIs will be sinking 2 points into it every cycle unless it's full already. And if the AI is down to only two or three planets left in general, then it's going to be spending 2 points per AI on each non-home planet, and 3 on the home planets (and whatever points exist beyond those per-planet caps just get wasted, which is another way you can technically influence galactic reinforcements, but since it requires taking almost all the planets it has no bearing except in really small maps or really insanely long games).
Anyway, there's a variety of things you can do here, as hopefully I've illustrated above, but it's more indirect rather than being more exact.