Anomalies and Obstacles can only be resolved by the active player at the end of one of their actions
(page 11) An empty sector is defined as a sector without any player units or colonies.
(page 12) You can only take an action if you can resolve at least one part of it.
(page 12) Each basic action (Advance, Recruit, Research, Colonize) can only be taken once per turn, but multiple times in a round.
(page 15) When you take the Government action, influence is not spent.
Certain effects allow you to initiate a battle resolution outside of the conflict phase. Here's how it works:
If the triggering component specifies a siege, conduct the siege step before awarding the medal. If no siege is mentioned, only perform the steps for placing the medal, battling with valid tactic cards, and claiming the medal.
Certain cards and effects allow colony invasions outside the regular conflict phase, such as Corruption Network (action card) and Incite Rebels (Emissaries module). When you invade a colony this way, you gain 1 military victory point, akin to a successful invasion/raze during the conflict phase.
Defensive tactic cards are not specific to any attacker. Defensive tactics fully apply to each opponent individually. For instance, if two attackers use Orbital Assault (each dealing 2 direct damage) against one Orbital Defense (blocking 2 direct damage), all damage would be nullified.