1 Peter 3:15 assumes that reasons exist and that Christians should be able to give them: "be ready always to give an answer to every man that asketh you a reason of the hope that is in you." The word for answer is apologia — the same root as apologetics, a legal defense. Peter expects that the faith can be defended with reasons. This implies that searching for those reasons is not an act of unbelief; it is the preparation the text requires.
Mark 9:24 is the prayer of a desperate father who is honest about where his faith actually is: "Lord, I believe; help thou mine unbelief." He does not wait until he has fully resolved his doubt to ask Jesus to act. He brings the partial faith and the partial doubt together in the same sentence, and Jesus works in that space. The faith crisis does not have to resolve before God can meet you inside it.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.