Any object on your layout can be moved around by selecting it and dragging it. This is true for fields, buttons, layout text and so forth. But variables have to be put in place as <<$$MergeVariables>>. They then can be part of a block of layout text that contains more than one merge variable and or merge field as well as layout text typed directly into the layout. So you might have a group of variables all inside one text object and changing their position relative to each other requires selecting the text tool and clicking that text object.
But objects can also be grouped and then dragging one drags them all. You can use the inspector to ungroup them if thisis the case.
And objects can be locked. Then they cannot be dragged at all until you use the inspector to unlock them.
There is no one place to go to to see all global variables defined in the solution. Variables are created in the instant a script step or other calculation--such as a conditional format expression using Let, assigns a value to that field. They will then exist and retain that value until their value is changed or the file is closed.