…and not to mention the parallel perpendicular locks as well. 
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and how to rotate in the direction of the group box blue lines? I marked in red the direction I want to rotate
That is probably the simplest of all, and has been mentioned already in this thread, use the Move tool and the rotate crosses that appear when you hover over the group’s sides.
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To be precise, you marked a plane, not a direction.
- as @Box suggested, use the ‘Move’ tool and find one of the four red crosses in the red marked group’s plane
- display the group’s axes (and local group origine) (an overall model setting) and drag the tool cursor along the desired axis direction.
The unfortunate reality is that despite your decade of sketchup usage you have missed many of the fundamentals.
You have recently posted a variety of threads, some asking for solutions to basic issues and others asking for extensions to avoid basic issues.
Learn the basics. Spend some time at the Campus and then come back with questions. We are happy to teach but ten years of naked twister is difficult to overcome.
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