2) I don't quite understand it either. Sometimes when I mouse over a hex near AI zones of control it tells me what % influence I have and what % they have, and other times I see nothing. Devs or those with more experience can hopefully explain.
to view comparative influence totals you cannot have any ship, base, etc selected. Also you need to point at an open tile not a base or fleet.
I don't know the formulas for how it spreads and adds up, but I can describe the behavior. Influence expands in all directions simultaneously and infinitely. The farther from the source the fewer points per turn. When two zones of control (zoc) meet they appear to stop moving and form a border, but this is an illusion. The influence is still going. So if the edge of your zoc hits an enemy mining base, which has a small bit of influence but that never increases, you will watch your influence appear to go around it and slowly shrink down its zoc. But if you hover over the tiles around the mine, you can see your own influence building in those hexes and if someone blows up the mine, all of its influence will go away leaving only yours. You won't have to "re-expand" starting at the old border. That's why I used the word illusion above.
Planets and cultural starbase generate influence every turn. All other starbase exert a one-time fixed amount of influence only inside their range. Cultural bases appear to match a planet (obviously racial mods, buildings, tech etc all come into play) with up to 15 population that is focused on production or tech. If it has multiple influence buildings or if it gets too high a population then a stock culture base is going to lose.
I find that three cultural bases with three culture upgrades surrounding a hostile planet can always culture flip it eventually unless it is immune.
Resistance appears to factor into culture flipping. If you are losing a p?anet to enemy influence then building culture upgrades is a long term solution, but it might not work fast enough. Instead, as long as you get over 100% resistance before your world goes to 100% rebellion you will not culture flip. THEN build the influence structures and start pushing back the borders. I do not know if the ai resistance works the same way or not, but I have confirmed this is how it works for the player and I assume it is the same for the ai.
If you have three world's you can check a tile over the course of several turns to see how much influence they are exerting at that distance. The planet window for each world also gives your base influence generation, but that is less helpful.
If you look at the "tactics" thread I put some detailed notes and screenshots on how to attack with influence. I'm no master, not by any measure, but I believe the advice is solid.