Yes, but you will most likely need an adapter to adapt the 2.5" drive to a 3.5" drive slot. Additionally, if you wish to keep it as an external drive and suspect/confirm it is the enclosure that is causing the problem, you can purchase 2.5" drive enclosures pretty cheaply.
cords are just copper connectors covered by plastic insulation
the bits that count are what is on the ends so if the end connections are the same , it will work
You might have to restore the backup files from on your Windows machine, then drop/drag photos to a new folder. Windows and Mac's use different filing systems, so Mac's are unable to read the Windows backup file format.