"1. Is there an option in diplomacy to demand that an empire stop its war against you? (There only seem to be options for demanding an end to specific sorts of attacks, not the war in general.)"
Demand a peace treaty.
"2. How does armour show in statistics? I add it to ships but I have no sense of its representation (i.e. another stat line in its description, for example) or how it works (i.e. do 10 armour points stop 10 points of damage from each weapon that hits it in a turn before being destroyed, or is it gone with the first 10 points of incoming fire it takes?)."
Each component has two kt Ratings- size and strengh. Armor components have a higher KT than their strength- armor III will stop about 40kt of damage for example. Once it's gone, it's gone.
"3. While I'm upgrading extraction facilities, do the ones currently upgrading still produce minerals, radioactives, etc., or are they offline?" Still produces. Same with everything else.
"4. I did a massive upgrade of my mineral miner plants from I to III (500 per turn to something like 1000 per turn). There appeared to be NO CHANGE in my production even though there should have been a massive one as far as I know; I kept checking stats under empire and it seemed to be stuck around 139k. What's going on?"
Hmm. Are you sure you weren't looking at your resource STORAGE?
"5. When ships are in formation how is their individual positioning in the formation being determined? (I want to be able to make sure certain ships are nearer the front of the formation, for example.)"
More or less random
except for the leader.
"6. Can boarders not attempt to board an enemy ship until the enemy shields are completely down?"
Correct.
"7. Under strategies, I don't understand the "damage" option where it says "damage percent per ship." Is this referring to how much damage my ships will take before attempting to flee?"
No, this is how much they'll shoot up the ENEMY ship before switching to another target.
"8. Do tractor beams actually work? I had three each on some destroyers and took them up against some enemy dreadnoughts. Didn't appear to do anything."
Only on ships smaller than the mounting ship. (maybe same size too)
"9. Do tachyon projection cannons actually work? I had TP IIIs on a veritable horde of small ships and took them up against said dreadnoughts but it appeared that the latter really didn't lose any weapons. I thought it would be the great equalizer given my small ships vs. the AI's heavily gunned ships. Are the cannons simply not worth it."
Yes, they work.. but they MUST do enough damage to destroy a weapon in a single shot. If they don't, the component will simply soak up fire infinitely.
Phoenix-D