The west perceives the mind be to separate from the heart, but in Hebrew idiom the heart is the seat of the intellect as well as the seat of the emotions. The heart is obviously something physical, not spiritual. Spirit isn't necessarily aligned with truth, eg the lying spirit of 1 Kings 22:22.
The spirit and the soul (mind, intellect, emotions) are two individual parts but make up the heart.
The Holy Spirit is part of God and is always aligned with the truth. Man’s spirit must be born again to be aligned with God’s Spirit (John 3)
The ideal of faith in the Christian tradition draws from Genesis 15:
And [Abram] believed in YHWH; and he counted it to him for righteousness.
Genesis 15:6
Yes!
This connects to the well-known chapter about the righteous servant, but the language is of gnosis (knowledge) rather than belief:
No The righteous walk by faith and not by knowledge as Jesus said to the Pharisees… you have a lot of knowledge but you don’t know the Father
He shall see of the travail of his soul, [and] shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities.
Isaiah 53:11
Yes… Jesus bore our iniquities
The idea that faith is spiritual draws from doctrine from John, but this word "is" is an interpolation, making the doctrine unreliable.
Actually… no. John, the disciple that Jesus loved and was taught by, understood quite clearly the Gospel as it was the disciples brought His message
Habakkuk 2:4 nBehold, his soul which is lifted up is not upright in him: but the just shall live by his faith.
Genesis 15:6 And he believed in the Lord; and he counted it to him for righteousness. (faith is believing)
Numbers 14: The LORD said to Moses, "How long will this people spurn Me? And how long will they not believe in Me, despite all the signs which I have performed in their midst?
Faith is the spiritual force of man (given by God). Knowledge is the strength of the Soul. Muscles is the powerhouse of the body.
And now you see what Gnosticism and the message of Christ don’t mix.
God [is] a Spirit: and they that worship him must worship [him] in spirit and in truth.
John 4:24, KJV
Yes… and without faith it is impossible to please God. Worship in the spirit is a worship in faith. Yes, you can and should also employ your soul and body… knowledge, emotions, mind, will and bodily strength.