No, you cannot control a territory that has your structure with enemy units on it. According to the rules, "A territory with a structure and enemy units is controlled by the enemy units' player." However, the enemy player does not gain your structure's abilities - they only control the territory itself.

Yes, you can place your 6th star immediately when you complete the requirement, even during another player's turn. According to the rules, you "place a star on the Triumph Track as soon as you complete one of the requirements," and "when a player places a sixth star, the game immediately ends." This means star placement happens immediately upon completing the requirement, regardless of whose turn it is.

No, Factory action spaces do not give bonuses that Player Mat spaces do. The rules specifically state: "Factory card action spaces do not give bonuses (Recruit, Structure, etc.) that Player Mat spaces do." Factory actions function differently from your Player Mat - they provide their own unique benefits but don't trigger the bottom-row bonuses you're used to getting from your regular Player Mat actions.

No, you cannot use resources from territories you don't control to pay for costs. The rules specifically state: "You may only use resources on territories you control to pay costs." You control a territory if you have at least one unit there (character, worker, or mech) OR if you have a structure there with no enemy units.

No, your home base does not count as a territory for any game effects, including end-game scoring. The rules explicitly state: "The Home Base does not count as a territory for any game effects." This means it won't contribute to your territory control during end-game scoring or trigger any other territory-based effects during the game.

No, you can only place one star at a time. According to the rules, when a player places a sixth star, the game immediately ends. This indicates that stars are placed individually, and the game would end as soon as you place your sixth star, preventing you from placing additional stars even if you completed multiple requirements simultaneously. You would place one star for whichever achievement you choose to claim first, and if that happens to be your sixth star, the game ends at that moment.