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Do I have to choose which space to explore before drawing the hex, and how must it connect?

Yes — name the exact empty space first, which also fixes which stack (I, II or III) you draw from, so you can't draw several tiles to find a good one. The tile must then be oriented so at least one wormhole connects to a hex where you have a disc or an unpinned ship; it doesn't have to match every neighbour.

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