Yes, you can do this. It depends on whether you run FMS as a two machine install or just a single machine install. I'd suggest in your case, a single machine FMS install would work fine. ( If not, then make sure you follow this instruction : http://www.goya.com.au/blog/two-machine-filemaker-server-installs-and-dns-issues )
For FMS and a completely separate web server, you need to install FMS as a single machine install but still enable the web components and web server. You then put a web server on the second box, and install the php API from the location you found above, and then alter one of the settings in the unzipped files. Details here : http://www.goya.com.au/blog/filemaker-server-and-linux-webserver
Once it's setup, you can firewall off access to the web server on the FMS box to only allow access from this second server.
Thanks Nicolas. I think I have it working now.
However I just included the files from
on my website.
The instructions here
tell me to install a few things with apt-get
which I didn't do. Also my site is on a rented webhost thus I dont have access to restart Apache.
But things seem to be working.