Is a young man considered a fiancé and does he have the rights of a husband over the girl whom he has pledged to marry and intends to marry upon his return, and is it permissible for him to see her without a head covering via the Internet?

A girl is not considered a wife to a young man merely by his promise of marriage. It is impermissible for her to see him or for her to have any spousal rights, due to the absence of a marriage contract. His statement, "You are my wife before Allah," is incorrect, as a marriage (nikah (definition)) is only concluded through offer and acceptance, with a guardian (wali) and two witnesses. The sister must fear Allah and avoid forbidden relationships with non-mahram (definition) men, as they bring evil and corruption.