I tend to think of GC2 as a "better son to Civ" than Civ 3 is

1. Switch "less greedy" to "more impressed with you" and I think you have the basic idea of diplo skill. IIRC, diplo skill can help you be less irritating when you make demands or reject demands. I'd also guess it means you get more bang-for-buck from gifts to AIs.
2. Alignment can affect relations w/ AIs, but in my experience it is oftene outweighed by other factors. I've been aiming for diplo wins in my last several games and I suspect that the "normal" course for that goal leaves you needing to wipe out a couple of AIs or at least help your allies clean up for you.
3. I'm misreading you, or you've slightly misread that dialog. The one I'm thinking of gives you the option of *decomissioning* all the ships of the class you just upgraded. I'd like a "Don't ask me again" check box b/c I've never once said yes to that option.
4. You get a "rep" from those events even before you formally pick an aligment, which can have diplo effects. You also have to pay lots of BC if you want to choose an alignment very different from the average of your choices for those events.
5. The underlying math is lost on me, but the influence you trade is indeed UP voting strength. Re UP "participation," so far we have no way to know about or influence what will be decided at a meeting. They're close to being random events.
6. I like to build as many Trade Goods as I can, because they give bonuses to your abilities. When you trade or give them away, the recipient gets the bonus also but only the owner of the planet can trade or give away the good. I tend not to trade or give them to AIs b/c I like having the advantage to myself, but they can be helpful when finagling stuff out of minors.
7. Play more games. You'll see armour on AI ships eventually. Especially if you play on Tough or higher, build a strong fleet, and arm your ships with kinetic weapons.
8. AFAIK, production time is about how many BC you can pump through a given starport. Size only matters in that big ships tend to cost more, at least when you pack them full of your best tech. A tricked out medium hull could cost more than a bare bones large one.