Sadly this is not possible due to the flatpatk sandbox, at least without having to rewrite basically the entire application. You can’t open other applications or shells from the sandbox, so nothing would work. Someone told me that it is possible in theory to reduce the level isolation of the sandbox via flatseal, but that would require the user to perform additional operations to make it even work. If it is not going to work out of the box, a flatpak version would not make a lot of sense.
There is an optional automatic update check included that will notify you when a new version is available. You can also automatically install the new version through that, but that is up to you.
For NX, I assume you're talking about this: https://www.nomachine.com/. I would have to look into that, it depends on how open the protocol and platform is. Without looking too much into it, I would assume it has some basic open component but since there is a company involved, there's probably some proprietary vendor lock in. It's probably the same as with VNC where there is an open protocol spec, but RealVNC also develops their own closed spec to lock out any third party clients from interacting with their tools.