Is there a way to get a file system on my Lumia 800 with Windows Phone 7.8? I dislike using Zune and would like to see and copy directly from my file manager. Is there a way to do this?
No unless you root the device.
In fact, it is impossible to have access to windows phone (either 7.x or 8.0) file-system for 3rd party applications (because they are sand-boxed and bounded to an isolated storage) and Microsoft has not provided such utility up to now (as far as I know).
Therefore there is no such utility application either on phone or even on PC. Zune sounds to be the only solution for syncing some sort of files (Music, Pictures…)
If you root the device then you may have access to file-system as there was on older versions of Windows Mobile and Windows CE.