Yes and Yes.
I always thought the source of all sin was pride, but it really is as Calvin describes, it is a lack of Faith and Trust in God. Adam and Eve's original sin came about because they lost their Faith and Trust in God, and in the process tried to strike out on their own. It seems to me that unbelief gives rise to pride and not the other way around.
There's a lot of truth in that statement. At times when I'm most worried and uncertain, that's when I have to stop and remind myself that everything I believe is really true. And because it's true, and because my faith is based on actual events, and because Christ really truly rose from the dead, I should have no fear.
And because of that assurance, I find myself capable of living a more generous, obedient life.
"We shall now have a full definition of faith if we say that it is a firm and sure knowledge of the divine favor toward us, founded on the truth of a free promise in Christ, and revealed to our minds, and sealed on our hearts, by the Holy Spirit...none hope well in the Lord save those who confidently glory in being the heirs of the heavenly kingdom. No man, I say, is a believer but he who, trusting to the security of his salvation, confidently triumphs over the devil and death, as we are taught by the noble exclamation of Paul, "I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord," (Rom. 8:38). In like manner, the same Apostle does not consider that the eyes of our understanding are enlightened unless we know what is the hope of the eternal inheritance to which we are called (Eph. 1:18). Thus he uniformly intimates throughout his writings, that the goodness of God is not properly comprehended when security does not follow as its fruit."