What is the way to get rid of the whispers of doubt about the existence of the Prophet Muhammad, may God's prayers and peace be upon him, and the existence of God?

Your dislike and aversion to intrusive thoughts (waswas) are a sign of the sincerity of your faith. Therefore, pay no attention to them and repel them by seeking refuge in Allah from Satan and by saying, "I believe in Allah." Continue to strive against your ego and persevere in your acts of worship, for your struggle will be rewarded. Do not let Satan convince you that intrusive thoughts prevent you from benefiting from worship or affect your answers in the grave, for all of this is from his deception to keep you away from obedience. Have a good opinion of your Lord and rely upon Him.