Is Hybrid Encryption CCA secure?
If the KEM is only CPA-secure, then the resulting scheme might not be CCA-secure. For example, consider a CPA-secure KEM that ignores the last bit of its ciphertext. Then it is possible to modify a KEM ciphertext in a way that doesn't affect its payload, which is enough to break CCA security of the hybrid scheme.

If the KEM and DEM are both CCA-secure, then the overall hybrid scheme is also CCA-secure. This is proved formally in Section 7 of: 


  Cramer, Shoup: Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack


However, it is possible to have a CCA-secure hybrid encryption scheme where the KEM is (slightly) weaker than CCA secure. This was first demonstrated in:


  Kurosawa, Desmedt: A New Paradigm of Hybrid Encryption Scheme


The weakened KEM security definition and composition theorem for hybrid encryption were formalized/generalized in:


  Hofheinz, Kiltz: Secure Hybrid Encryption from Weakened Key Encapsulation