1) For the life of me, I cannot figure out how to destroy a previously built logistical structure in order to make room for a new one. How do I do this? I've tried everything and nothing works.
To scuttle, there is a yellow caution looking bar below the picture area, bottom center of the hud. By default I believe the hot key is shift+s, but you can change it in the key bindings menu.
2) Towards the latter part of the game, I keep losing my planets to culture loss. I've noticed that the opposing factions colors comprise most of the travel lines to my planet, is this the reason? I have tried to counteract this by placing broadcast centers in the further planetary systems where my allegiance is low. But even my planets closer to my capital get effected and turn against me. Which leads me back to question "1", I usually don't build broadcast centers in my closer planets, but then it's too late because my logistical slots are filled and I can't delete a pre-existing trade port, refinery, etc.
Culture is usually pretty easy to repel, having 1 culture center every 2 jumps or so usually works. You might need more if your opponents built a lot on the front line. Also the Advent Superweapon has the ability to spread a lot of culture from where it hits, if you don't have a lot it might cause that after repeated hits.
Also, if you need more time to fortify your culture, capitalships can repel culture away from a given location. Keep a few near planets that are about to be over thrown, it may help.
I've been also getting hurt late game by the novalith cannon. Is it imperative that I build and use these first... before the opponent gets it? Is there another way to counteract those?
Each race has a starbase upgrade (TEC's is called Axillary Government) that prevents a planet from being lost to bombardment (but not culture) so long as the starbase is alive. This includes from Novalith cannons. As soon as you get the superweapon building warning, build some star base constructors on your main planets to protect them and their expensive upgrades. Usually the AI will waste some shots on the pirate base or something, but still its good to have them ready.
4) Are starbases more important than turrets and hangars? Does placement of these matter (closer to the planet or closer to the phase-jump line)?
Repair bays are actually the most important defensive structure, combined with a starbase. You might have a hangar or two to keep bombers off your starbase, or if you wish to use their researchable upgrades, but you won't need a lot.
Generally you want to group all of your planet structures together, so that the repair bays can cover them and the starbase can fight off anything attacking your expensive labs, trade ports etc.
5) When playing with a friend, how am I able to get our loyalty points raised, so we can engage in more pacts? I've tried to give and receive credits, metal, crystal. That didn't seem to work.
You both need to research and build envoy cruisers and send them to each others planets. They are the only thing that can increase relation points above 10. If you have less than 10, other things like sending resources will increase it.
6) Can enemy envoy cruisers actually prevent you from building ships if they are sitting in your planet space? If so, how do I counteract this? I know for sure that at one point in a game I was unable to attack it and I think I couldn't build either. But maybe I just did something wrong. It was frustrating.
I don't think it was the Envoy cruiser doing that. 
Unless you were using a mod, envoys can only help allies. They can make themselves invulnerable for a period of time, but they shouldn't affect your buildings.
