- Should be fine. The “atomic”-ness of Bazzite is in the OS, not the user-writable data, so applications aren’t “atomic” in the same way, unless they’re in the base image (e.g. Steam).
- Flatpak is recommended first, before any other method, so in a sense, no, but since there are limitations in that version (e.g. screenshotting doesn’t work), it’s fine to install it using another method.
I’ll answer 3 and 4 together: if the application is a fully self-contained executable file, either AppImage or a golang binary, then it’s fine to just put it in a bin folder on $PATH, but for something distributed as many files (in a tarball or other archive format), it would be tidier to put it in a Distrobox and export it. The way you’ve got it working is fine, but updating and uninstalling are more straightforward with Distrobox: you just delete the container, and if updating, create a new one and install the new version in it.
One caveat: I use the Flatpak version myself and just work around the broken screenshotting, so I don’t know whether anything extra has to be done to make screenshotting work from within a Distrobox container.