Thanks!

This is an excellent list of potential issues.

"What are you going to use to actually encrypt messages? You don't want to directly use the public key primitives to do this."

I'm not sure what you mean by this.

Could you explain why there is a need for another encryption protocol beyond a public/private key encryption?

If the protocol is secure against brute force attack, both the public key and the encrypted messages could be open and would not create a vulnerability to the private key.

What am I missing?