To be sure of x64/64-bit or x86/32-bit, press Windows Flag+Pause/Break and take a look at the
System type: section.
As for FLAC audio on Windows Media Player, you will need a codec to play them.
By far the easiest thing to do is go to Ninite and choose the
K-Lite Codecs option. This will install K-Lite in the bare minimum configuration and should add FLAC support to Windows Media Player.
If you do not want to use Ninite, here is a link to K-Lite's homepage.
Also, if you haven't used it yet, I would highly recommend you take a look at VLC Media Player (Also available on Ninite). It allows FLAC audio out the box and you don't have to mess around with any messy codecs!