Illegal thing in chess

LOL - I think if your school gave themselves a more time they may find a worse idea. What identify an illegal move, because your opponent seems to have played 3 illegal moves. Also, any slight change in chess would just devastate the whole game concept, in example if chesscom implemented a take back feature under premium, even if for once in a game it would be just a complete disaster.

My guess is the intent of the ruling was that the illegal moves, if made, would be taken back and a legal move be played, but more than two would incur a penalty.
Your opponent can never move one of your pieces and should only touch your pieces if taking them.

Have I missed something here???
What you missed is Martin_Stahl's explanation (comment nr. 4).

I don't understand this. If illegal moves are legal then every position is checkmate. White loses on the first turn by checkmate without moving ... literally every one of the black pieces have the king in check because they threaten to (illegally) take the white king. White doesn't even have time to (illegally) capture the black king on the first turn because it is in checkmate before it moves.
Have I missed something here???
Yes, when an illegal move is made it must be taken back and a legal move must be made instead.
So my school conducted an OTB Chess tournament. They've set a rule that a player can do 2 illegal moves before losing the match. I played against an opponent who made one illegal move. So, my king was on d7 and my pawn was on e7 (I was playing white). His rook was on e1 and his king was on g7. But, when I placed my pawn on e8, he took the pawn, gave me his rook, and he moved my king to another square. Does this count as an illegal thing to do?