Concerning your central question, Yes. Faith involves the will as well as the intellect. It is an act of submission to God’s authority. Some theologians of a Calvinistic / determinist bent have said that faith is involuntary because the will simply does what the intellect perceives as good (rather than informing the intellect what is good). While it is true that on one level the intellect moves the will, in another sense the will (as governing principle of the soul) moves the intellect, as in the act of faith. (For the theology behind this, see S.T. I, Q. 82, a4.)
As to the translation, I don’t know Greek, so I will leave this to the experts.
Ver. 25-27. Now to him that is able, &c. These three last verses, in divers Greek copies, were found at the end of the 14th chapter, where we find them expounded by St. Chrysostom. — According to the…mystery kept secret from eternity, now made manifest; he means the mystery of Christ’s incarnation, and man’s redemption, formerly revealed indeed to the prophets, but now made known to all nations, in order to bring all men to the obedience of the gospel, by embracing the faith and doctrine of Christ. (Witham)
As to your question:
“Faith” which is the complete acceptance of GOD"S TRUTHS [limit one per defined issue] in an absolute sense depends on humble Obedience.
God has zero interest in OUR opinions, our personal views of His Teachings, and grants everyone sufficient grace to discover HIM, through His Truths.
Ultimately only love can compel obedience. This, love, is what faith is meant to lead to. But we can be like demons who, although they believe, tremble. Here’s St Basil of Cesarea:
"If we turn away from evil out of fear of punishment, we are in the position of slaves. If we pursue the enticement of wages, . . . we resemble mercenaries. Finally if we obey for the sake of the good itself and out of love for him who commands . . . we are in the position of children."
Faith is the doorway to justice, but if Adam had truly loved God- with his whole heart, soul, mind, and strength-then his justice would’ve been complete, and he would never have disobeyed; obedience would’ve flowed of its own accord…