Attacking AES/CCM with random IV
No.  The attacker cannot easily recover the secret key.  The attacker cannot modify the ciphertext to something that decrypts to some other plaintext.  This remains true even if the attacker can encrypt an arbitrary number of chosen plaintexts.

This is known as "IND-CCA2 security" (security against adaptive chosen plaintext/ciphertext attack).  CCM satisfies that notion of security.  So too do other authenticated encryption schemes, like EAX, GCM, etc.