Is it permissible for a young man to correspond with a chaste, religious woman via social media, given that she is the age of his mother, and with the motive of reassurance or discussing certain problems, without prolonging or repeating the correspondence?

A man's conversation with a non-mahram (definition) woman is permissible when there is a need, provided that there is no fear of temptation (fitna) and that Islamic guidelines are observed, such as the woman not speaking in a soft or alluring manner. However, conversing with her without need is impermissible. Considering her to be like a mother in age does not justify the conversation, because Satan might exploit that to lead into temptation. Safety is unparalleled.