Is correspondence between a young man and a young woman—friendship through messages—which includes general discussions and some affectionate words like "my dear" or "I missed you," considered impermissible (haram), or is it permissible (mubah) with adherence to respect?

In Islam, there is no relationship between the sexes outside the confines of marriage. The Holy Quran has forbidden taking "illicit partners" (akhdan), as Allah Almighty says: "—marrying them, not for unlawful sexual intercourse or taking [secret] lovers" and "—marrying them, not for unlawful sexual intercourse or taking [secret] lovers." The exchange of messages and phone calls falls under the forbidden category of taking "illicit partners" due to the corrupting influences that result from it. Therefore, you must cut off contact with this young man and repent to Allah.