Will Allah Almighty hold the one who suffers from intrusive thoughts accountable for the thoughts and laughter that come to him against his will, and will he be pardoned, knowing that he does not recite the Shahada or perform Ghusl due to his intrusive thoughts? Is his action correct?

We advise you to turn away from whisperings (waswas) and from thinking about them, for thinking alone does not hold a person accountable, and the laughter of one afflicted by waswas is of no consequence. The Shahada (declaration of faith) and Istighfar (seeking forgiveness) are prescribed at all times, but what is more important is to strive against oneself to get rid of the whisperings. Your hatred of these whisperings and your aversion to them are a sign of the sincerity of your faith, as the Prophet, peace and blessings be upon him, said: "That is pure faith."