You seem to think a SfY app on a different platform would not be taken down. Apple took the app down after a simple letter from the patent holder. The patent holder could have asked for relief in court, enumerating the infringing apps. IANAL, but that's a common request in patent cases, and usually granted by the court. All app stores would have to comply then, however free (or non-totalitarian), maybe even removing the already installed apps.
It could be taken off the Android market, but Google doesn't forbid alternative installation modes. It's not foolproof, but at least with Android you own the software and can install it without having to go through a corporate monolith like Google/Apple.
From a country with no software patents? IANAL either but I don't see how this could be stopped, especially in case of an app whose development had been funded via donations and which is distributed free of charge.
Say, they do distribute it this way and are found guilty of patent infringement. Would they then need to pay for each copy downloaded? I have no idea how this works, it would be really helpful if somebody with some knowledge could chime in.