2. If you are sure that you are not connected to the Internet, you can play games on the memory card normally and win trophies, or you can keep playing until you want to change a batch of games or start playing genuine cassettes.
3. The use of other network functions also requires you to log in to the psn account, so whether the use of other network functions is always normal is risky. For example, if the psn account used by the seller when buying a game is blocked or he changes his password, you will not be able to connect to the Internet. If you change another psn account, your current game will not be available.
To sum up, if you play a stand-alone game, there is no problem. If you still want to connect to the internet, then register your own account to buy a download version of the game or buy a cassette! I hope I can help you.