How to show Hash-Then-Encrypt is not AE-secure
first one is simple as ${H_1(m)}$ leaks the information about the message in the ciphertext. So it is not CPA secure.

second one , the scheme will be under CCA. as @SEJPM mentioned attacker can modify the c1 such that new ciphertext c2 will be the result of ${H_2(c1)=c2}$, so ciphertext integrity is not preserved, required in AE.