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Magnet can handle all standard resizable windows in OS X for you. Magnet can not do anything with non-standard windows used by some developers. Fortunately, such windows are quite rare. The only notorious example is Adobe Creative Suite. You can not manage those apps except for Adobe Acrobat.
Certain apps require a minimal width of their window. In some cases the width can exceed half of your screen, particularly on small screens like Macbooks'.
Magnet is compatible with OS X 10.8 Mountain Lion or later. If you can run such OS X, Magnet will be working fine on your Mac.
You can arrange your windows in any active Spaces screen. You can not do it across different Spaces.
The Mac App Store probably just got confused by all the certificate, signature and security stuff. Simply trash your Magnet from the Applications folder and redownload from the Mac App Store. There’s no charge and you will keep your current settings.