Answer : 3. "3"
Explanation :

do (Aux. V.) will not be used because – Each clause has to be structured in a way that is a complete sentence on its own. Look at the structure below : I never considered him to be a person who would go back on his promise. (Sentence I) I never considered him to be a person who would not even apologize. (Sentence II)

Combining the two sentences – I never considered him to be person who would go back on his promise and not even apologise. Hence, not even apologise is the right usage. Use of – would do not even apologize is incorrect.