Is it possible to use an Android phone as network disk, so I can browse it on my TV?
It should be possible. You would certainly need root.

If you could mount your network share onto your phone, you could mount it under /mnt/sdcard/network_share. Then your tv would simply browse that folder. To your TV, it would simply look like another folder on your SD card.

This post shows how to mount nfs on your phone. You may need a special version of busybox.

busybox mount -o nolock,ro,hard,intr,vers=3 -t nfs 192.xxx.xxx.x.x:/your/nfs/share /mnt/sdcard/network_share