1. I attempted this once, and gave up in frustration. There are so many interconnected factors involved it's too hard to isolate one variable to create a workable equasion. I'm sure with proper computer support and plentiful time someone could solve it, but I didn't have the resources available to devote to it.
2. In general, population trumps buildings. From what I saw in the failed attempt above, total civilization population also plays a substantial role in the influence generated by individual planets. I quit before I looked into whether this goes off absolute population or proportional population (eg. whether your empire pop being 1 trillion matters, or that you have half the total population, that sort of thing).
Getting 14 pop is generally a good endpoint. If you have a couple bonus tiles, or several morale mining bases, or significant passive bonuses from other sources (preferably all three of these) you can usually get to 20 before seeing real morale problems. This assumes a PQ 11+ planet for the high-quality planet bonus.
3. Short answer: No one can really tell you, as it will vary wildly based on the surrounding environment.
Long answer: see #1, although this part is easier to approximate than trying to solve the influence production per planet. You can treat each planet as a point source of influence based on its current influence production. The influence generated decreases with distance (roughly linearly, as far as I can tell) from the source generating it. Every planet (and starbase, see below) generates whatever influence it's going to so that turn, then the total influence on every space is totaled up. Your border is drawn at the point where your influence is greater than anyone else's on that particular space. When going into empty space, the border is drawn where the influence field drops to a certain value (presumed to be 1, never really tested).
All starbases except terror stars create their own influence, but most never grow much. Influence bases generate their own influence and the modules you stack on them boosts the BASE'S influence, not that of nearby planets. Unlike planet influence, starbase influence decreases with distance squared (again, not rigorously tested, but definitely non-linear). So when it comes to placing bases, the best place to put them is touching whatever you want influenced, whether defensively or offensively.