Is it permissible to read the Quran in public places, trains, and buses? And is ablution (Wudu') required when taking out the Mushaf to review verses?

One should refrain from raising one's voice when reciting the Qur’an in places of disobedience, such as markets and gatherings where there is immodesty and naked images, out of reverence for the Qur’an and to keep it away from such places. However, there is no impediment to merely looking into the Mus'haf (copy of the Qur’an) in such places, provided it is not accompanied by raising one’s voice. Purity from both major and minor ritual impurity is required to carry the Mus'haf, as long as one is carrying it.