What is the ruling on one who attributes to Allah Almighty characteristics that are impermissible, knowing that they are impermissible, but these are thoughts that come to him, and he has tried to get rid of them but has been unable, and he seeks forgiveness whenever he remembers them? Has he fallen into shirk (polytheism)? How does one know that? And what should he do if he has fallen into it?

It appears that what was mentioned in the question is from the whispers and intrusive thoughts of Satan. A person is not held accountable for inner speech and obsessions as long as they do not speak or act upon them, for the Messenger of Allah, peace and blessings be upon him, said: "Indeed, Allah has forgiven my Ummah for whatever they whisper to themselves, as long as they do not speak of it or act upon it." A person does not fall into shirk merely by whispers, but rather by speech, action, or belief that contradicts faith. As for one who attributes impermissible qualities to Allah, they must repent, seek forgiveness, and utter the two testimonies (Shahadatayn) if they have indeed disparaged Allah Almighty. It is advised to read the Quran with contemplation, maintain daily supplications, and occupy one's time with what is beneficial.