1. pop income yes trade income no

2. yes

3. Max increase is at .07% not affected by stations

For Vanilla Sins, the maximum alleigance of a given planet is determined by its shortest distance to your homeworld (in phase jumps). These values are starting alleigance values - they are the values the planet has immediately upon colonization (this can of course drop or increase in accordance to influence to hostile/friendly culture respectively).

0 Jumps (i.e. your HW): 100%
1 Jump: 90%
2: 80%
3: 65%
4: 50%
5: 40%
6 or more: 25%
-1 jumps*: 25%

* The only time a planet has -1 jumps as its distance from home planet is if the shortest (and only) route goes through a wormhole, which can be a challenge in maps with planets isolated by wormhole connections. It's most noticeable on the map Ancient Gifts, where travel from one system to another MUST be done via a wormhole - there are no links to the stars of each system.

Culture can up the values by 10%, the Advent's Allure of the Unity tech can increase this further by 5%/10% depending on research level.

Once you start talking about Entrenchment, I believe the Advent Starbase can bump alleigance even further up, but since I'm not an Entrenchment player, don't quote me on that.

Culture spread rate is a function of the number of broadcast structures in a gravity well, the culture rate of one station, and the number of phase lanes connected to that gravity well.
-- Spread rates of multiple broadcast structures add up (so 2 stations have double the spread rate of 1, three have triple the spread rate of 1, etc.).
-- Culture rate is determined by how much research you have put into culture spread rate. All broadcast structures generate culture at 10.0/sec initially, but can be upgraded to 12.0/sec for TEC and Vasari, 13.0/sec for Advent, and increased by 25% by the Manifest Dominion artifact.
-- The culture generation from one gravity well is distributed evenly among its connected trade lanes, so for one station broadcasting at 10.0/sec with one phase lane connection spreads at 10.0/sec, 5.0/sec with 2 phase lanes, 3.3 with 3 lanes, and so on.

thought the SB added 30%. weird.

A minor correction, its:

3: 70%
4: 55%

Yeah, tradeport income is not affected by allegiance.  But tax & resource income is.  Simple culture can raise your allegiance (and therefore income) by 10% across the board, resulting in the following regression:

0: 110%, 0 Jumps (i.e. your HW)
1: 100%  1 Jump
2:  90%
3:  80%
4:  65%
5:  50%
6:  35% 6 or more Jumps

And culture has additional benefits for each race (with appropriate research), it boosts:

TEC antimatter regeneration
Advent shield mitigation
Vasari damage output

If you select a planet, its infobox will show its current Allegiance (as a percentage, right there on the top). The infobox will also show the 'Culture Rate', if a media center is present.

I'm not sure I understand your other question, or whether it can be answered, but the following might help.  One culture center (media station) provides a total spread rate of 10/sec, which is divided by the number of phase lanes leaving the planet.  So a planet with 4 phase lanes would show a culture spread of 2.5/sec, which I believe is halved as it passes thru the next planet.

I mean... How can I know if an enemy culture is affecting my world?

Edit:  Ah, nevermind, I had my question answered in another post.  Mouse over tells you more information.