While there are a lot of (hot)keys not yet in the game, this post is not about that.
The "Done" button/action in the shipyard is not bound to the "Done" key. The default binding in the Options->Input for the "Done" key is "Enter".
The "NextNotification" key (default the "Tab" key) also invokes the next turn. While it should take you to all outstanding actions, but not end your turn. To go through all the outstanding actions and thereafter ending your turn should be limited to the "RequestNewTurn" key (default bound to the "Enter" key). So it appear that the "NextNotification" key action is bound to the "RequestNewTurn" action.