What information to include when calculating the HMAC of ciphertext
Yes, it is best to include all that information in the HMAC. Otherwise an attacker can change those values and you would not get the correct plain text. This would mean that you get either incorrect information, or you leak information that could be used for padding oracle attacks.

In case of the IV, if you don't include it in the HMAC then the attacker can change the first block of plain text you get when you decrypt the first block (assuming CBC mode encryption here).