Will a person be held accountable for obsessive thoughts of insulting Allah and the Messenger, and do such obsessive thoughts invalidate prayer?

You are not held accountable for mere thoughts that the heart has not acted upon, due to the Prophet's (peace be upon him) saying: "Indeed, Allah has forgiven my Ummah for what they whisper to themselves, as long as they do not act upon it or speak of it." You must turn away from them and not dwell on them. Prayer is not invalidated by this, but its reward is diminished. To rid yourself of the devil's whispers, persist in reciting the Mu'awwidhat (Surahs Al-Falaq and An-Nas), the morning and evening remembrances, those after prayers, and before sleeping. Also, increase in supplication and humble entreaty to Allah.