Does the influence border affect the influence or reverse? A practical example: I have two equal planets, one in the corner of the starmap and one in the center position. What if I build a cultural capital in one of them? Will I have the same infulence growth?
Influence affects the border. The border is calculated by summing the influence contributions of all planets and starbases (yours and others), accounting for the fall off of value over distance. The border is drawn where your influence from all sources is 1 (when bordering empty space) or when the value of your influence at that point is greater than the next highest civ (where the ratio of your influence compared to theirs crosses the 1 threshold).
Remember that influence drops, IIRC, by the inverse square law from its point source and that the point source value is what population, capitals, modules, etc. are all affecting.
Not true. Influence from starbases drops as an inverse square function. Influence from planets is closer to linear with distance (I still haven't tested this out thoroughly, but there is a marked difference between the two).
Yes, I understand what you are saying, the best way to use a cultural capital is to push back the influence of the others by putting it in a crowded position. My question is a little theoritical in this way but it is still that kinda: If I simply want to raise my number of votes in the Council what would be the better choise for the capital: the center or the borderline of the map (that way I'd get a half-circle) or is it the same?
For the purposes of flipping planets and influence victory, the crouded area is better, assuming there are enemy planets nearby. For straight UP vote production, identical planets will have identical results. Given a choice, put it on your most populated planet to get the highest number of votes, and the greatest effect on flipping and victory. Influence production scales directly with population on a per-planet basis.
IOW, putting the political capital in crowded space may not increase your votes all that much, but it might well decrease the votes of the other races there, making the true delta larger than might be expected.
It does not work this way. Votes are created based on their influence output, regardless of how much territory they own around their planets.