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1: a player wants to or has to take a marker implies that a player is required to take the markers produced by his ship's configuration. Is this correct, or can a player take fewer energy markers than his ship produces?You have to take all energy markers that your ship produces.
2: If I take a free action turn (whether or not I wanted it), do I still have to put one of my cubes on the turn track?Yes.
It's called a free action turn, since you get to collect energy "for free" before taking the action turn. Maybe a better name would have been "free collect energy turn" ;-).