Mounting a remote folder as local folder
On a rooted phone you have several options -- via 3rd party app, directly through a unix mount command, see How to mount SMB/CIFS Network Shares on android device?

If your phone is not rooted, I do not know how to do that, maybe there can be some app on a play store that is able to mount a network share (NFS, SMB, FTP, ...) via normal privileges (it is definetly possible under unix).

If you want to share just music and/or video you can use DLNA (your phone does not have to be rooted for this to work) -- install a DLNA server on your PC/router and than something like XBMC for Android or BubbleUPnp on your android device.