1. Has been answered above
2. Building influence starbases is one way though on the higher difficulty settings the AI starts to get annoyed if you build starbases near it's borders. Another way is to find planets that have an influence enhancing square and build an embassy on it. The other thing you can try to do is find Influence Resources and mine those. There are also techs that will increase your influence production.
3. The best advice I can give for building ships is to build whatever counters what your enemy is building. For example if he is building ships with beam weapons then you build ships with shields. Also if he has armor defenses but no other defensive techs then you might want to build beam or missile weapons. Early on it isn't very important that you get more then one weapon and one defense on a ship. As you get larger hulls and go up the weapon tree it becomes possible to put more then one of a type on a single ship. Also as you build ships put them into fleets. They are much more affective together then they are alone.
Don't try to mix different weapons or defenses on one ship. If you want to have variety in your ships build two or three versions of the same ship. I usually put together all the ship bling I want and then at the end slap on the weapons, engines, defenses, and modules I wanted. Then if I want to change the loadout I simply upgrade that ship replacing what I want and then rename it so the old one is still available too. It's quite fun to watch a fleet rip the enemy to shreads because it counters their build perfectly.
