All normal building only work for the planet it's built on.

All trade goods work empire wide and can only be traded once (per race and you can't aquire same goods twice).

Super projects and galactic achievements are a bit trickier but mostly its written in their description if they work empire wide (like the Restaurant of Eternity or just for the planet like all capitals.)

The trick to having a better military, economy ,tech and influence than the computer is to colonize anything you can regardless of the PQ because if you spend so much time looking for 26 class planets you'll never get anywhere. Colonize every planet in a solar system and assign each planet to a certain job. The front line planets (close to a civ) should be manufacturing and influence.

So build mostly factorys and put a starport you could also put your manufacturing capitol there, focus all of your production on Military You will use that planet for building your ships(also a starport on every planet isn't necessary). The influence one should be mostly embassies and anything influence like. The planets facing the direction inside of your civilization should be economy tech and population.Put all of your money improvements there. For the tech put your labs there and for the population make lots of farms and entertainment centers (this will give you votes in the UP and give you tax). So thats just my strategy it works on most of the difficulties and the comps get stomped whenever I use it.

I've never traded any Trade Goods, either, because I've been unclear on whether I'd be giving away all of my Magic Beans, or just sharing them with the other civilization.

I mean, it's obvious that the Trade Goods I have made work for me: My ships fly faster, my teeth shine whiter, my wives notice that little something extra -- but what isn't obvious is that I can trade it to the Drengin for a Mickey Mantle rookie card and a Mess of Potage and still keep enough of it for myself to make my wives happy and my teeth shiny.