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Cutting down those trees is pointless; you can just build up your army. I couldn't do it at first either; he has a standard-sized army, and it doesn't increase over time... Can someone post a screenshot? I don't understand whether I'm blind (which is unlikely), or if I don't understand which shipyard we're talking about, or if my game is bugged...
You need to buy the "Summon Ship" amulet in the corresponding building, go down to the water below the castle, and summon the ship.