Is the son obligated to obey his father in not going to the mosque to review the Quran with a sheikh, under the pretext of the father's fear for him, and is this obedience considered disobedience to Allah? And is it permissible to review secretly if obedience is obligatory?

If you can review the Quran with a شيخ (sheikh) without angering your father, then do so. If your father's منع (prohibition) from going to the mosque has a valid purpose and his fear is genuine, then obedience to him is obligatory. However, if it is merely a misconception, then obedience is not obligatory, and you should seek a means to review (the Quran) without angering him. Your not going to review with the sheikh is not considered a sin شرعًا (Islamically) because it is not an obligation.