Thank you for your post.
When you select "Open Remote..." from the File menu, it will search for all shared database files in your local network. It will not search external networks. One solution is to add the IP address to your "Favorite Hosts". That way, you can select "Favorite Hosts" from the pop up and access the files.
"Open Remote..." showing "Local Hosts" will only display FileMaker Pro (and FileMaker Pro Server) instances that are sharing databases if they are on the same local subnet. Apple's implementation of ZeroConf (Bonjour) is used on both platforms to advertise and browse available databases (it will be installed for you on Windows) without having to enter the IP addresses manually.