I would like to play couch coop on my PS4.
I have read lots and see that I have to buy a second copy. I am okay with that.
Will I have access to D4 on all of my PS4 accounts?
When I purchase D4 on PS4 on an account not connected to a battle.net does it create a new battle.net account?
Ideally I would like to be able to play couch coop with the same characters that I play on the PC.
All progress is stored on your Bnet account from what I understand. To play at all, you need a Bnet account tied to the PS4 account. You will want to ensure you link your PS4 account to the Bnet account that has your progress.
Otherwise, your progress is not accessible.
You can read this Tech Support post about issues people have run into when linking is not done right, or is changed.
As for accessing D4 on all your PS4 accounts. I can’t speak to that. I don’t work for Blizz or Playstation and don’t use consoles so I just don’t have experience with that.