CCA security of this scheme
I won't give the answer; here are some hints:


Suppose we have a valid cipher text $(A, B) = F(k, r), r \oplus F(k, m)$.  What happens if we modify the ciphertext to be $(A, B \oplus C)$ and get that decrypted?
How can we use this?  What can we do if we have two ciphertexts that encrypt the same message $m$?