If I buy a game from Playstation Plus, will it save on the PS4 or the account? Will my other users be able to play the game even if they aren't subscribed? Can they play online due to my sub or will they not be able to play it at all?
If you get a free game from your PlayStation Plus membership, it will be tied to your account.
You can add these titles to your library without actually downloading them at that time.
If the PS+ account is the primary account for the console, yes, all other users on that console have access to the game. If your PS+ account is not the primary account for the console, then only that account will have access to your games.
As others have mentioned, if you let your subscription end, you will lose access to the games you were given for free. However, I believe that they are still tied to your account, so if you renew your membership, you will regain access to those titles.
If you purchase a Playstation Plus game when you launch the game it will check to see if the purchasing account is still tied to your PS4 so in short, yes you can play your Playstation Plus game on a different account on your machine, as long as your account with Playstation Plus is still on the system.
The only time you won't be able to play your Playstation Plus games is if you let your subscription end which will not let you play your games anymore until you resubscribe.
Any games that are bought from the Playstation store are tied to the PSN account, not the machine. Local users to the machine should be able to access and play the game, but may not have all of the capabilities of the account from which the game was bought on.
These games are no longer accessible if the PSN account subscription expires.