Your messages are secured with 256-bit end-to-end AES encryption.
No one can impersonate you or your friend: Diffie-Helman key exchange with secret message sharing avoids Man in the Middle attacks and makes sure that you are chatting with who you meant to chat.
We have no idea who you are or who you are chatting with what-so-ever: Since messages are transferred over Google Cloud Messaging service and you do not connect our servers directly, we do not have any information about you, your IP or your phone number.
Google cannot see who are you are chatting with. It can make some intelligent guesses though, if not enough number of people are using Eagle :).