How can one achieve salvation from repeatedly falling into sins and prove the truthfulness of the Islamic religion?

Whoever doubts that Islam is the true religion disbelieves and exits the fold of Islam, because believers are those "who have believed in Allah and His Messenger and have not doubted." One must beware of the suspicions cast by enemies and websites that sow doubt regarding the rulings of Islam, especially concerning women. It is impermissible to look into such matters except for one who possesses firm knowledge and strong faith. The fundamental principle is to believe that Allah is All-Knowing, All-Wise, All-Just, and All-Merciful, and that His rulings are based on wisdom. As for what whose wisdom is hidden, its knowledge is entrusted to Allah. When Satan whispers, one should say, "I believe in Allah." One should be keen on acquiring beneficial knowledge from the Qur'an and Sunnah, performing righteous deeds, associating with good people, and avoiding evil ones.