Quantum

You win immediately when you place your final quantum cube on the map; dominance at 6 merely lets you place a quantum cube immediately (and can be used multiple times), but the instant-win condition is placing your last cube (p.3, p.5).

Ships move orthogonally up to the number on their die and cannot pass through or land on planets or other ships; you may attack by ending your move on an enemy's square, and only the Interceptor (or card effects) lets you travel diagonally (p.3, p.4, p.5).

No — if an attack is repelled the attacker is not destroyed and dominance does not change; dominance only changes when a ship is actually destroyed (p.4, p.8).

Constructing a quantum cube uses 2 actions and requires your ships to be in the planet's orbital positions (the four orthogonal adjacent spaces) whose die values add up exactly to the planet number; diagonally adjacent ships do not count (p.3, p.4).

Each ship can use its special ability only once per turn even if its number changes; you can use the new ability only if the ship has not already used an ability that turn (p.5, p.8).

You get advance cards in the Advance Cards phase after finishing your actions — one for a research breakthrough (research die = 6) and one for each quantum cube placed that turn; gambit cards take effect immediately while command cards become active on your next turn (p.3, p.5, p.8).