'Save a Copy As...' is disabled on hosted files, probably to protect users from unadvisable things such as you're trying to do.
Copies can be made by transferring files using the file system. Make sure your database is closed when you do that. To iPhone and iPad you could use iTunes.
Synchronization is an issue, that sooner or later will give you (big) problems.
I understand your (financial) hesitation about Server. You can - however - create a "server" configuration using FileMaker Pro. All you have to do is leave one computer permanently on and host your file on that machine. If you open appropriate ports and fiddle with NAT on your router this will work even over the internet.
You may also want to investigate some of the synch tools offered by 3rd parties such as 360Works and SeedCode.