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Yes you should be able to because both consoles use the same digital audio converter. Just use the optical like you do with your Xbox. Be aware though that the PS4 won’t be able to provide atmos support like the Xbox does as according to my own research, Sony didn’t program the console to support Dolby’s atmos format. Beyond that though you should still be able to get digital 5.1 and likely even 7.1 surround off the PS4.
Yes, but not the mix amp.
Correct me if I’m wrong but you could plug in the mix amp to your PS4 to get game audio only. But if you want to use the mic, you need the mix amp specifically for your PS4. You’re better off buying this product that says PS4 as each Astro mix amp have different modules for each console. Or buy a mix amp if you can’t buy the headset/mix amp. Mix amps go for about $150 at the Astro website. There’s more information about this on YouTube from multiple sources such as Tmartn.
Astro makes headsets console specific. For instance this headset works with Xbox One and PC and the other version works on PS4 and PC. Because they go through the trouble of making separate models for each console I would assume the Xbox version does not work on PS4