How can a Muslim help non-Muslims enter Islam, or marry a non-Muslim woman, given the prohibition of befriending and loving them, and does this contradict Islam being a religion of love and peace?

A Muslim should pursue ways to strengthen their faith. Asking questions to remove doubts is commendable, as long as it's not out of obstinacy or to stir up suspicions. Allah has commanded us to disavow disbelief and its adherents, and to show loyalty to faith and its people. However, this does not preclude natural affection for a disbeliever due to kinship or kindness, provided that disavowal of their religion remains. This natural affection does not contradict religious enmity. The true test appears when the two types of affection conflict, at which point love for Allah and His Messenger must be prioritized. Hatred for a disbeliever is not due to their lineage or color, but due to their disbelief. Nevertheless, this does not prevent one from desiring their guidance. Combining disavowal of polytheism and hatred for its adherents with mercy towards creation and striving for their guidance is the reason for the excellence of this Ummah. And Allah Almighty may create affection between Muslims and their former enemies.