Faith is the ascent of the mind toward a mysterious presence of the one who is the origin of all creatures, namely God. It is the acceptance of all God has revealed because he is the supreme Truth.
Now, did Christ have to believe in God? Since Christ being God already contemplated God face to face, he did not need faith because he already enjoyed the vision of God. Faith is a prelude to vision and vision is the realization of Faith.
Did Christ hope in what God had promised? Hope is the desire to possess God. Since Christ was God intimately involved in the life of the Trinity, he already possessed God and it would have been impossible for Him to hope in what God had promised, namely the vision of God in Eternal Life.