For the flash receiver I would use something like:
No.
The AR series lights are not X-system compatible. They use Godox's "FR" protocol - so you would need the FT16
https://www.amazon.com/Godox-Wireless-Channels-Reciever-Speedlite/dp/B015OAJCV8
The problem is that (I think?) their FT system is their older stuff and they don't make any Sony compatible triggers for it.
Get the Sony compatible X system trigger - because their X system is their current generation and almost everything else they make supports it. Then get a second Godox light that is X-system (and Sony) compatible. This can be something as simple as a Speedlight. As a side-effect, this gives you back HSS and TTL which while you might not need right now you will find uses for later.
The AR400 has S1/S2 modes, so, use your X trigger to talk to your X-system compatible light and let that light trigger your AR400 for you.
I have a couple of old, generic "universal" speedlights - the kind you find at Walmart for $30. They have S1/S2 -- and I use this exact setup to control them off-camera, as they make excellent (and stupidly cheap) hair/rim/accent lights.