Is total assent to the Catholic Faith necessary for a valid confession?

Must one believe and know the Catholic faith to be absolutely true in order to receive forgiveness through Confession?


Here are some examples:
Sally Smith is a baptized Catholic, though lately she's been having some both voluntary and involuntary doubt of her Faith. Is it possible for her to validly confess her sins, including the her sins against Faith, feeling sorry for and wishing to discontinue her sins against Faith, while still desiring to attain certainty that her Faith is true, but not yet believing with certainty that her faith is true, and consequently not entirely believing in the validity of the sacrament of Penance itself?

Johnny Appleseed is a baptized Catholic, but is in a state of mortal sin. He wishes to have the Virtue of Faith, but as he is in a state of mortal sin, he feels uncertain of whether God will grant him the grace to receive this Gift of the Virtue of Faith. Since he does not yet have the Virtue of Faith, and lacks absolute certainty and assent to the truth of the faith, must he make a valid confession before opening himself up to God's grace to the extent needed to receive the Virtue of Faith, or must he first accept the Virtue of Faith and then go to confession?

Thanks for any help anyone could give me with this question :)