Hey,
Regarding the WinWing - it ought to work just as it does with the Moza software on Windows.
My software just talks to the base for the effects; that is to say, it outputs force feedback info from the computer (sim) to the base.
The input (from the base to the sim - you move the stick, you press the buttons, etc) is handled by the standard OS drivers just like any joystick. FFB-Bridge is not involved in that.
So as long as the joystick works as a joystick in Linux, without FFB-Bridge running, no feedback, just a regular joystick - if the buttons work here, it should work with FFB-Bridge running.
Please note that I cannot guarantee this without testing the stick myself; this is not the final word. But I'm pretty sure it will work as it does in Windows with respect to the buttons.
For firmware - no, FFB-Bridge will not incorporate this. I'm not trying to build a replacement for Moza's software, and doing firmware updates and all can get tricky. All of that is best handled by the manufacturer. I treat the Moza as just another stick FFB-Bridge sends force output to, and I just make sure that FFB-Bridge knows how to initialize the Moza so it can receive the data. I do not touch any firmware or any Moza specific settings. So yeah, if you need to update firmware you'll have to use Moza Cockpit (or maybe there are linux tools for this? No idea).
DCS/IL2/WarThunder/EliteDangerous/P3D/FSX/Condor and more are all on my "maybe" roadmap. That is to say, I would like to support as many sims as possible, but it all depends on what's possible - if the sim doesn't output the correct data, nothing I can do. Some are easier than others. I know P3D and FSX should be possible as they are quite similar to MSFS, just older. For the others, it's going to take me a few weeks to investigate whether it's possible to do.
So on that one, check back in August to see what's up. I hope this helps, feel free to ask more questions!