Can I move / copy within SharePoint / OneDrive for Business?

Yes, it is possible move or copy documents within the same library or between libraries (in the same site collection).

Items can be selected by using the checkboxes or the mouse (similar to Windows Explorer). Pasting can be done by using a checkbox and typing CTRL V or using the right-click option "Paste".
Items can also be moved copied using drag and drop via the mouse.