There are other ini's like scripts.ini that MediaMonkey uses, so I can't say that it would be okay to remove all others.

I'd only copy the database (it includes the Playlists) and setup everything else again. The following guide can help: http://www.mediamonkey.com/wiki/index.php/Moving_MM_to_a_new_computer

Thank you - I've identified the one that has the most recent date. Okay to delete the others?

Also, I want to move all the tracks, playlists and everything relevant to MMG to another hard drive (external), how do I ensure that I correctly move everything that is needed and nothing that isn't?

Look at the Modified Date.

Also see: http://www.mediamonkey.com/support/index.php?/Knowledgebase/Article/View/16/0/modifying-the-mediamonkey-db-and-ini-files

For some reason, I have a few of the above files on the hard drive, how do I find out which one is the one being used by MMG please?