So basically i don't need the bin folder, gw2.exe (probably 32bit) and it's .tmp (probably bound to repair or something, today i made a repair of my 64 and my -64.tmp is dated as today).
Not sure about the Local, ArenaNet and THIRDPARTYREADME.
About Screens Folder, mine too is in another folder, but this one is empty, so nothing i need to clear.
About Music Folder, i never tried custom music and don't know how it works, maybe someday.