My mobile phone changed the number of the SMS center. Do I have to pay for playing mobile games and sending messages?

You should be happy that there is no charge, because the charging system in your mobile phone or software is imperfect. Generally, famous brands can't play games if they change their center numbers, that is, they can't send messages; And your ability to send shows that you can play for free. I suggest you turn off Monternet business and be safer.