@markyluv
It's been awhile since I created my account for use with Battlefield 3 but at that time simply loading the game prompted me to create an Origin account.
I have no reason to believe that the game won't prompt you to create an account if one is required to play so you should be able to quickly create one through the PS4 but you could also create one using your PC if needed.. In the event that you do have to create an Origin account be certain to use the same email address which is associated with your PS4 account, doing so usually means that any logins will be done automatically in the future, including when you first load any future EA games which require such logins.
If you still have the redeem code for the Deluxe bonus content then you should be able to allow any of the accounts to redeem it, bearing in mind that it will only apply to that account. Unless you're a completionist who really needs or wants to get the game to 100% the perks included with the Deluxe version aren't anything that you can't live without; there is an exclusive Imp character, some exclusive customization items and character abilities and of course the big chunk of coins to get you started.
When playing Co-Op Player 1 will go to the stack of two television sets next to the Dressing Room where you select and customize your characters. When selecting that there will be a prompt for Player 2 to select their PS4 account OR continue as a Guest. If Player 2 selects to continue as a Guest then nothing will be saved for them but if they select their PS4 account then everything they do will count towards their progress- XP, Stars earned, unlocks, and so on will all be applied to their account and will be there the next time that they play.
A couple of notes about Co-Op play: the game features some story elements and Multiplayer options which are intended for Single Player mode and activating Co-Op mode, or having someone 'visit' your Backyard Battleground will lock out all of this material. This means that the "L.E.A.F Agent" and "Top Zombie" missions will become unavailable, no online Multiplayer or online Co-Op can be accessed and this will include accessing the hidden Trials of Gnomus portal and the Mystery Portal which is available inside Town Hall when the doors there are opened. There is also a special "Solo" mode in Garden and Graveyard Ops which allows you to select up to 3 AI Teammates- Co-Op mode won't allow you to buff out your 2 Player team to 4 with AI helpers.
The Multiplayer Portal will be accessible during Co-Op with the "Private Play" option and you'll be able to play against AI opponents with your team filled out with AI teammates as well. It's not as challenging as human opponents and teammates and doesn't award quite as much XP but you do get the same 12 v 12 experience.
You should also bear in mind that during Co-Op Player 2 cannot interact with various Backyard Battleground elements such as Prize Chests, while Player 1, who will be designated as the Group Leader, will be able to open those Chests for themselves. This also holds true whenever you visit another Players Backyard Battlefield- you can only open the Chests found in your own Backyard and whenever you are in another players Backyard the Group Leader determines which games you actually play as any other Players in the Backyard are dragged along with them when they start a game mode.
I am also a PS4 Player by the way and should anyone need or want in-game assistance you can add me as realitysquared on PSN- some of the game modes, like Infinity Time and the Mystery Portal event called "Boss Hunt" can be challenging.