Is it permissible or forbidden to supplicate to Allah for a lawful marriage? And should a girl continue communicating with a young man who sends her religious articles, or should she cut off communication for fear of Allah's wrath?

If by your supplication you mean that Allah grants you a husband and that there be affection and love between you, then there is no objection. However, if you mean establishing a love relationship before marriage, then that is a supplication for something forbidden. You have erred by corresponding with the young man via email, and you must completely cease correspondence with him and avoid mixing with non-mahram men unless there is a need. We advise you to supplicate that Allah grants you a righteous husband.