Ps4 – Does logging out from a user account also log out the PSN account

For primary accounts on a console there can only be one per account. When you make a new PSN account on his console this will make that PS4 be your primary console (I believe it does this for brand new accounts). You will not be able to do cloud saves without paying for playstation plus, but your trophies will be saved to the cloud by default since it is related to your PSN account. To answer your questions directly:

1. This will not damage your friends PSN account.

2. This will not do anything wrong to his account or PS4, though when you get your own PS4 you will need to deactivate your account as primary on your friend's PS4 (if by chance it is primary) or you will not have access to any purchases you may have made or will make.

Yes, PSN accounts are different to ps4 accounts. You can use your PSN account on as many ps4 user accounts as you like. The ps4 user accounts only contain your game saves, so deleting a ps4 account will not delete the PSN account linked to it or it's subscription. And if your worried, just log onto the other ps4 account with your game saves with your PSN account, no need to delete the new one if your worried.