I'm replying to expand upon a couple of Annatar11's statements.
1. Trade ports: Is it worth building more than one per planet?
It's worth more to build 1 each on 5 planets, than 5 on one planet because the longer a trade route you can make, the more each individual trade port will earn. (exponential-ish)
More than one on each planet will add the same income per trade port as you are already earning. (linear)
In general, it is best to fill your logistics slots, so go ahead and build more trade ports if you have the room and don't need a lab or factory or something.
2. Culture structures: I'm still a little iffy on culture. In my games thus far, I've mostly relied on military power, (In fact, in my first 2 matches, I never built any culture structures at all) but I've recently started playing around with culture a bit. Should I build one in every system and is it worth building more than one in the same system?
As Annatar11 said, you don't need one on each. One every other system is plenty to get the Alliegence boost from culture, and I space them out a little further than that, usually every third system if the phase layout allows, so each strucutre is supporting the planets around it.
5. What's a good 'hangar-to-gun' ratio in regard to orbital defenses?
This one is trickier. Hangars and guns have roughly the same DPS, but hangers cost 4x the tactical slots and 2-3x the material costs, but also cover the entire grav well and can change their damage type to suit their opponent (fighter or bomber), while turrets only defend their little section and are static in every respect. I think they are perfectly balanced for their roles, and so I build them on an equal slot use basis. Repair Bays too. Therefore, on a 15 slot asteroid, I'll have 1 hangar, 2 repair bays and fill the rest up with turrets. For 25 slots, I get an additional hangar, and another repair bay or two, plus a few more turrets. Make sure that some turrets cover the planet to shoot at siege frigates, and that the repair bays are covering as much as possible, but also protected by the turrets too.