Will I be able to read-write an external HD with APFS on a Snow Leopard machine?
This is an interesting question that might affect me too. I often boot into target disk mode to move files to an older Mac, sometimes even one that's PowerPC for updating purposes. So yes, I'm curious to know what Mac OS versions will balk at reading an APFS drive.
No, unless someone comes out with a FuseFS driver or a user-client driver for APFS. Especially for PowerPC machines.
Will APFS mess upp things for 3rd party applications in the way that files are handled?
Yes if the application requires that the volume be case-insensitive. HFS+ is case-insensitive by default, but AFPS is not. I know Photoshop has issues with case-sensitive volumes. But in general, this is rarely an issue. I know someone who used case-sensitive HFS+ with tons of third-party stuff and only had problems with Photoshop and Steam, nothing else. And it's not hard for devs to fix this.
UnrealEngine 4 also has this issue.
Not only is it an easy fix for developers, the question is why would a team insist on making case-insensitive volumes a requirement? Especially for cross-platform apps!
Besides this minor issue, I don't think there could be other problems, but someone can correct me if I'm wrong.
The filesystem should be transparent to most apps, unless they need special integration with file or volume metadata (such as forks, Finder-specific data, etc.).