1. atm, the only real way to win the game is to destroy all of the enemies planets, or destroy enough to make him surrender (depending on if you are playing entrenchment or not) as it stands, AI in entrenchment tend to surrender more than in the original version. However, with the new x-pack being developed, there will be new and different ways to win the game, i assume via culture, economy, and sabotage etc, at least
2. so, culture is spread by broadcast centers (each race is called something different but meh). the more you have at a certain planet the faster culture spreads/the slower it retreats (if at all). however, there are researchable upgrades that improve the effeciency/speed of culture spread and reduce culture loss. each race has different upgrades. The Advent are culture masters, so if you were playing against them, you would have to have a decently strong culture to resist. Other factors that affect culture are any Capital ships and or Starbases in orbit. these slow enemy culture from approaching your planets, and help speed up culture loss at enemies planets with no culture centers.
The way it works is there is an allegiance value attached to all your planets. this value is affected based on: how far that planet is from your homeworld, whether it is connected with trade ports or not and friendly and enemy culture spread (i think i got them all, im not sure) the further a planet is from your homeworld, the easier it is to be lost to enemy culture, as the max allegiance value is already much lower than normal, so make sure you have a broadcast center at or close to your border worlds. a planet is lost to enemy culture when your allegiance on that planet reaches 0. the planet then becomes neutral. i think thats all you need to know about planet loss and culture... ask if you are still unsure
3. culture will spread to other worlds at a speed depending on research done and how many broadcast centers are nearby. you dont need to build it on every world, but on/close to your homeworld, and on/close to every frontline planet is a very wise strategy, as well as a few in the center of your empire.
think of it like this. you want to fill an ice cube maker with water, but your tap is broken and only lets out a trickle of water. if you use one tap, each cube thingy will fill up with water slowly until it overflows into another cube thingy. but, if you want to fill the ice cube maker as fast and as completely as possible, optimally, you would get between 3 and 6 taps to trickle water into each corner of the ice cube maker, as well as in the middle. this fills up the ice cube maker much faster, and much more completely than with the 1 or 2 taps. its not a perfect analogy, but its roughly correct.
about spammable structures, youd be better off spamming trade ports first, and refineries second, personally, i place trade ports along the most optimal route, and a few other planets, and refineries at ice/volcanic worlds and worlds next to UCGW (UnColonisable Gravity Wells) with neutral extractors in them (its like a resource asteroid you find at your normal planets, but located in a gravity well like a debris field or plasma cloud etc
hope that answered your questions 
