Ok here we go:
1. PS4 games downloaded from the PSN Store are linked to an account, not a PS4, So.. if you delete the account that came with the PS4, the games they bought will be deleted(you will not be able to used them until you re-purchase them on your new account).
2. Unless you know the email and password for the account that your PS4 came with, you will not be able to change any settings on that account, like emails, passwords, (PSN account name cannot be changed)
3. If you are able to log in to your own (new) account and play the games that the other account downloaded (and the games do not have a small lock on the bottom right hand side) this means that the account that came with the PS4 is already set as PRIMARY on this PS4. Meaning that ALL other users will be able to use both the PSN PLUS, and their downloaded games, with out any problems. Meaning, that you will be able to use your account, and you now have 5 free games.
4. If under your (new) account, you try to open the 5 games and they have locks, then this means that their account is not set as Primary on this PS4, so you need to log into their account -> hit the UP arrow, -> Settings -> PlayStation Network/Account Administration -> Activate as primary PS4 -> Activate ... You would not need their password to do this. Once you set the account as Primary on this PS4, you now have free 5 games to continue playing on your main (new) account.
Let me know if you have any further questions.
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Potential exploits? SO far there has been only 1, based on web browser, but on versions so old, that at this point almost no-one has them. So, I dont think there would be any exploits coming to the PS4, nor that it could ever be hacked, maybe in 5 years. You should be just fine connecting to the internet and playing online, feel free to update as hopes of hacking the PS4 are slim.