Dr. Peek is indeed the Director of Admissions for Fordham Rose Hill. Has been there in that position since 2012. Her direct email address is however different than you listed, though perhaps they want responses to go into a different basket instead of flooding her personal email address with applicants responses, leaving it for other university business.
Fordham does reach out to students both domestically and internationally. Doing so however does NOT imply they guarantee admission. Its the start of a conversation.
However, I dont know about the FordhamU.org website. That seems odd. I am suspicious. Fordham almost always uses the Fordham.edu email address for every department. Typically Fordham Admissions is enroll@Fordham.edu.
I would copy and send your alleged email to the enroll@Fordham.edu email and ask if it it is legitimate and why they are using a FordhamU.org email. Maybe its legitimate and used only for admissions, I dont know. But verify before you reply and send off something personal to them. Hackers abound around the world and someone may have gotten her name and used this bogus email address.
Good luck.