Is it permissible to marry a Christian woman over the phone who will convert to Islam, given that her parents are deceased, and can the marriage officiant be her guardian?

Marriage is not valid except with a guardian (wali). The guardian of a Kitabiyyah (a woman from thePeople of the Book) is her disbelieving guardian. If he is absent, then the Muslim judge undertakes her marriage. This is according to the Shafi'i school. As for the Maliki school, they hold that if the disbelieving guardian is absent, their bishop marries her.

It is not permissible for the contract writer to be the guardian. It is permissible for the suitor to look at the fiancée in the presence of someone who negates privacy. The wife must be specifically identified and known to those who will bear witness.