1. When man fell, did human intellect fall with him?
2. If yes or no... to what extent should we trust human reason and human intellect?
The mind is a part of the soul, thus we must manage it as to which Spirit influences it. If God has control of our lives spiritually, by way of Spirit to spirit in our innermost selves we have His wisdom coming thru the spirits revelations given to us by God Himself. But God then wants us to place our minds in Christ. Common sense is not spiritual discernment, nor is it part in parcel of it either. it is diametrically opposed to God, by way of the flesh - by the devils influence.
The good news is - God restores our minds in Him if we allow God to finish His workmanship in us thru the Holy Spirit. News Flash: If we do anything outside of the Holy Spirit's influence there is no spiritual value there at all. Thus, with the fall of man, and the Cross' sacrifice by Jesus our spirit has come alive, and our flesh must be muted a slave in the power of God's Lordship; The things of the flesh being put to death.
This includes never being passive in our minds. For Satan only needs a Christians mind to be passive in Christ to take ground there. A great subtle trick he uses often for those who are stagnant in righteous living. Satan would love us to not think at all and to just let him put godly reasoning in for us. Then, we only have to act upon that reasoning, for there is no other reasoning in there ... But, God would have us use our minds actively for His Name sake, and He created man's mind for just such a purpose, as we live by the Spirit/spirit now in our new creation rooted in Christ Jesus. We must remember the body has been sentenced to death along with the flesh, but God can restore the body (not the flesh) to serve His will even though it was what sinned against God, in Adams case and was sentenced to death when we physically die.
If a mans mind is in Christ, surely we can trust it. If it is a mind outside of righteousness, no matter how godly it sounds, it is of no value to the Kingdom of God because it is outside of the Spirit of Christ, and cannot be trusted - ever.