Is a marriage contract concluded via telephone and mail, in which a guardian is appointed for a new Muslim wife who has no mahram, considered a legitimate contract?

A marriage contract via telephone is not valid. However, appointing a proxy for it is permissible. Furthermore, children are not obligated to obey their parents in marrying someone they do not approve of, as long as she is religious and of good character. If the parents agree to this woman, then she should appoint a man to act as her proxy for the marriage.