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If you were to have a solenoid (0 current) floating still in space, and shot a magnet through it, would the solenoid move, or would it only create a DC current (what if it has a closed/open circuit)? Does the magnet slow down (if so by how much)? What if you increased the speed/power of the magnet drastically, would anything change?

(Feel free to link anything that could help explain solenoids/E&M fields better.)

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No current, no back emf, no reaction force if the solenoid circuit is open. But if you close the circuit by shorting the solenoid input leads you will see current, and a reaction force. You need a closed loop to have current flow

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