Is the AES-GCM encryption using the SHA256 hash of the plaintext as IV secure?
No, because in order to decrypt it you must pass along the SHA-256 hash too, and now you have leaked a public function of the original message, which an adversary can use to efficiently test a guess offline about what the original message was.

If you want a deterministic authenticated cipher, you might consider an existing construction like SIV that has been studied already.