Is it permissible for a young man and a young woman to continue communicating out of necessity after agreeing not to speak to avoid God's wrath, and is their return to speaking caused by Satan or by God's will?

Any emotional relationship between a man and a woman who are not mahram (definition) must be severed, as it is not permissible Islamically. Conversation between non-mahram individuals is a cause of fitna (temptation) and is only permissible out of necessity, while observing Islamic etiquette. A young man's conversation with a young woman about her private problems is not a necessity and can be an opening for Shaytan. Caution must be exercised until Allah facilitates marriage, and only Allah knows the unseen.