Does security against a CCA1 attacker imply security against a CPA attacker? I've seen it mentioned multiple times, but have not seen a formal proof of how security of an encryption scheme against a non adaptive chosen-ciphertext attacker (under non-malleability or ciphertext indistinguishability) implies security against an adaptive chosen-plaintext attacker. 

Does IND-CCA1 imply IND-CPA (and NM-CCA1 imply NM-CPA)?
Simply consider the two games and a reduction between them. From the contapositive you need to show that every attacker against CPA yields a CCA1 one. Now, from every CPA adversary you can always construct an adversary that breaks CCA1 but simply makes/requires no decryption query (clearly the same holds for CCA2).