Hi Beinhard,
Up until now, F5 hasn't supported the use case for LTM to serve web content itself. It can be done in a very limited fashion using iRules to serve a handful of images and some HTML, but it's not on the scale of a full webserver. If you think this could be useful, you could open a case with F5 Support to document the request.
NFS mounting isn't supported natively, but it might be something you can configure. You might need to manually add packages to do this. F5 wouldn't support it if you did got it working, but there isn't anything I know of stopping you from trying.
Aaron