What should I do about the severe reproach from my family and my mother because I advised them to stop listening to music, to adhere to Islamic dress, and not to shake hands with non-mahram men, and because I reminded my father to pray, and bought Islamic and literary books?

Continue to advise your family with wisdom and good counsel, using an approachable method. Clarify to them that what you are inviting them to is the religion of Allah. Be careful that your advice does not anger your parents, and envelop it in a gentle, compassionate style. Strive in supplicating for their guidance. As for buying books, you can balance it with saving, such that you only buy what you need, and utilize the books and resources available online.