I don't know if this has ever been brought up before, but I see no reason it would be banned. Current runs accept the bonus soldiers you get from a GZ save file to help boost your army, so the GZ suit should be allowed as well.
It's allowed. You'll just have to do the run in Offline Mode. Don't think online is required for carry over soldiers or Definitive Experience's DLC Mother Base Soldiers. Not 100% positive though.
You don't have to access MGSV's online/FBO play or Metal Gear Online to get your GZs bonus stuff, no. If the saved game is already there then it will access it automatically; otherwise you have to back out to the menu and download the GZs data, but that doesn't connect you to the online play server. It does take a few seconds, but it's probably cheaper than buying Ground Zeroes on PS4 and 100%ing it again.
