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  1. Yes, that is a correct interpretation of the output.

  2. The way you have drawn the figure, Q is equal to (y2 - y1), or the change of the y component of the robot frame with respect to the fixed frame

What is Q, in the context of your application?

Also, this is not really related to laser_scan_matcher, but looks more like a general trigonometry question, or at best a question on robot motion models. Maybe this reference would be useful.