How can one repent and get rid of the many ugly thoughts about Allah and His Messenger, peace and blessings be upon him, some of which are considered worse than disbelief and from which there is no repentance?

These thoughts do not harm you, no matter how great they are. Your dislike and aversion to them are proof of the soundness of your faith. Do not pay attention to them and turn away from them. Know that they are from the whispers of the self that Allah has overlooked. To get rid of them, strive against yourself by not indulging in them, seek refuge in Allah when they come, and stop thinking about them. You will be rewarded, Allah willing, for your struggle to get rid of these whispers.