When you move the cusor over the planet you get an info box. In that info box is a line that says how much culture is being 'produced' by that planet (if you have a broadcast Center or equivilant structure). Also, if you select a planet, in the three little boxes just to the left of the planet picture on the HUD, the middle one tells you the current alliegence (I have no idea how to spell that
). If you move the cursor over that box, it will tell you the max alliegence, current alliegence and the rate and direction of change (better allied, or if enemy culture is present, lossing alliegence). You can do this with enemy planets as well as along as there is a scout, remote sensor, or fleet there. Advent can see this when their culture reaches an enemy planet, as long as the proper research is done.
Your capitol ships also affect alliegence, and if you mouse over those, you can see how they are affecting it as well.
i think you get the bonuses if the line is going up to the planet
You get the bonus before the culture line actually reaches your planet. As long as there is enough 'force' behind the culture spread to make it to that planet.
Hope this answers some of your question, Erictred1.
Sawakaki