Should a girl continue to desire marriage to a young man in whom she has observed bad character, such as his looking at pictures of naked women, despite repeatedly seeing him and hearing his name after performing the Istikhara prayer?

This istikhara was not in its proper place, as the young man did not propose to you. The sign of istikhara is the facilitation of a matter or its absence. A believing woman should not accept a young man who is ill-mannered and of bad character, and who looks at pictures of naked women. One who does not observe the rights of Allah cannot be expected to observe the rights of His creation. The Messenger of Allah, peace and blessings be upon him, said: "If there comes to you one whose religion and character you approve, then marry him. If you do not do so, there will be tribulation on earth and great corruption." We advise you to turn away from him and ask Allah to provide you with a righteous husband.