Could someone familiar with the American tertiary system help here, and give their opinion on:
1. I DON'T think this should be done by email, as proposed.
2. If you write, then it should be to the Dean of the Graduate School, not just one of the professors in the School.
3. Wouldn't they expect a prospective PhD. applicant to be aware of the staff of a School, and their area(s) of interest and expertise, and so, at that level of academic study, expressly wish to work with that Professor because of his reputation/research writings/academic tomes? ...not indicating to them you intend to apply without having basic knowledge about the School?