Does the duplicated stack have any relations with the original stack?
No, a new instance is being created. All blocks become new instances and do not point to existing blocks. 

Does it work with global areas too?
Yes.

Does a global area become a normal stack when duplicating?
Not by default. You can, however, choose the stack type. That way you can copy a global stack to normal stack and vice versa.

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Currently the dropdown only supports up to 200 stacks.