Hi @christopher2KLSVU
I hope you are doing well! Here are my answers to your questions:
Q1. How to easy move polygon from Layer 1 to Layer 4.
A1: I think you can select the polygon and then change the layers in Inspector Dialog, like:

Q2. How to move crazy polygon shape in one shoot within a layer, how to catch it and move, entire shape?
A2: Sorry that it has a bug issue here so that you can't Press Shift to Move the Whole Polygon now. And the bug will be fixed in the October Release. And I will keep you updated.
Workaround for it: You can Select the Layer the Polygon On from the Selection Filter and choose Polygon Edge in the Selection Filter. Then you can group select the whole Polygon and then try to Move

Q3: how to set, rename Layer 1 as layer 4?
A3: I am not sure the Layer 1 and Layer4 here. If it is the name of the Polygon, then I think you can just use Name command to Rename the Polygon. And if the Layer 1 represents Top Layer, then I think the answer is in A1.

I hope I don't misunderstand your questions here. Please check if the answers can solve your problems, thanks!
Regards,
Panpan Fan