Ps4 Online ID account question. Is it possible for a random PSN users to know about your suspension (the breach of the tos)?

No, the records are not available publicly. Only a PlayStation employee would have the ability to view that information 

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As stated by previous answer input - however there is also another way - if you have told people via your facebook account that this has happened and you are not fully private - or you tell a friend who tells and friend who tells another friend and by the rules of the six degrees of separation and unknown person to you knows about your suspension. Recently a player of Fortnite was banned for using Aimbots in the game - he foolishly posts video doing this and people see he is using an aimbot and then he is surprised when the game makers and Sony banned him.