1. It depends. If you have more than 2x the number of ships that the AI does on that planet, then yes you want that AI Eye dead as soon as possible. If you're the lesser power, or you're on equal footing for the moment, it can wait.
2. Hitting F1 toggles through five pages of that and your normal planetary summary. You can also use Shift+F1 to jump right back to your planetary summary.
3. It really varies, often by what is isolated and what is not, and what your forces are like and what the AI's forces are like. See #1 regarding the eyes. For ion cannons, if you have a lot of low-level non-starship ships, that's probably an early priority. If your ships are all higher-level or mostly starships, maybe not. A big priority is always getting rid of all the guard posts, as killing those reduces the amount of reinforcements the AI can get at the planet -- but you want to balance that against whatever is killing you the most. If there's a huge pocket of a lot of guard posts with overlapping attack ranges, maybe hit something more isolated first. Or, maybe stir them all up and get them to intentionally attack you on your planet, so your turrets can "play goalie" and clean up. Various guardians or guard posts are stronger depending on the types of ships you have, too, so that's a consideration when you attack each one. Others may have more specific comments.
4. It depends. Usually not, but if you have an AI Exo-Galaxy Wormhole on your planet, then yes. Also, if you get hit by a counterattack wave from a CounterAttack Guard Post, that could also do it. Also, cloaked enemy ships could be slipping past your defenses and appearing there, or regular ships could even be breaking through without your noticing it -- I've lost several games that way. Having tractor beam turrets, and possibly even tachyon beams if you think it's cloaked ships, will help prevent that.
Glad you're enjoying the game!
