Could anybody correct my grammar, please?

When Mr. Botibol awoke the next day after the auction and realized that the sea was as smooth as glass, he felt very distressed and started to consider ("thinking" I believe is also correct, but I think this is more natural) if he could do something to delay the ship. Time was passing, he grew more and more nervous and, on top of that, any idea came to his mind (I do not follow what you mean with this last bit). Suddenly, Mr. Botibol began to hear shouts from the window of his cabin. When he came out, there was a flutter of excitement; everybody was running side by side, there were children crying, and everybody was shouting. He tried to figure out what was happening by talking to someone, but, despite his attempts, he couldn't. Then he realized that the problem was that someone had fallen from the ship. Automatically, he began to feel anxious and hopeful again (anxious and hopeful are two very different feelings - are you sure he felt anxious and hopefuly simultaneously, are you looking for different adjectives?). He knew that it was the opportunity to delay the ship and probably win the auction, so he sat (down) to observe how the men were trying to rescue the victim. The rescue lasted two hours, two hours of delay that made Mr. botibol happy.

could anybody correct my grammar, please?

When Mr Botibol awoke the next day after the auction and realized that the sea was as smooth as glass, he felt very distressed and started wondering if he could do something to delay the ship. The Time was passing and he was getting more and more nervous. and On top of that, all sorts of ideas  any idea popped into his mind. Suddenly, Mr Botibol began to hear shouts from the window of his cabin. When he came out, there was a flurry of excitement, with everybody running side by side (do you mean "from side to side"?). There were children crying and everybody was shouting. He tried to talk with someone to find out what was happening but, despite his best efforts, he couldn't. Then he realized that the problem was that someone had fallen overboard.  Automatically, he began to feel anxious and hopeful again. He knew that the delay to the ship's journey had given him an unexpected opportunity to win the auction. So he sat down and observed how the men were trying to rescue the victim. The rescue lasted two hours: this meant two hours of delay and that made Mr Botibol happy.

[Wow - you write very well!  Check my changes to your punctuation as well. All the best, Michael]