Is it obligatory to inform the owner of the PlayStation store that payment for past gaming sessions with him was not rendered, while taking into consideration not to embarrass the friend who used to work for him, and is it sufficient to return the money without informing him, and is it necessary to pay for everyone's gaming sessions or only the questioner's, and how should the due amount be estimated?

The way to ascertain whether playing for free is authorized by the shop owner is to ask him or your friend. If you wish to pay for the time you played, you are not obliged to inform him of what you did. Rather, you should convey the value to him by any means, estimating it in a way that you believe will clear your conscience. Your conscience is also cleared by the shop owner's forgiveness and pardon, and it is not a condition to disclose your identity when seeking forgiveness. As for guaranteeing the value of your colleagues' play with you, you are obligated to guarantee it and return it to the shop owner if it was not authorized, because each person involved in usurpation is accountable for the entirety of it.