Biker, you ask a great question! I'm not sure I can adequately address it; and I know I don't have the time to address it now.... I'll get back to you.
Here goes. (Disclaimer: I'm not a mighty theologian, but only a humble Christian who still is learning the depths of the grace of God, as He guides me in my experience of it.)
First, in terms of "is it necessary to believe?", I would make a distinction between belief and faith. Everyone believes something. Even the atheist, as has been pointed out in this thread, believes that God doesn't exist, and has thereby staked his eternal destiny on that belief. Other's believe in other things: ideals, values, ideologies, the supremacy of capitalism over socialism, whatever. But the point is that every person not only is capable of belief, but by necessity, exercises that belief in some way.
But the essence of belief is that it is seated in the mind -- the things we believe are comprehensible to the mind. Faith is another matter, and is different than belief. Faith is a matter of the heart. Faith is the ability to place one's trust in something, even when that something may seem beyond reason.
Regarding the nature of faith, it isn't so much the faith which is important, but the object of the faith, or the focus of the faith. And faith is usually something we direct toward someone else, to perform something for us that we cannot perform ourselves. When you get on an airplane, you do not walk to the flight deck and take over the controls yourself. You put your faith in the flight crew to get you from point A to point B safely -- they perform something on your behalf which you cannot perform yourself. When you go to see a dentist, you are putting your faith in that dentist to drill a cavity and fill it properly -- you don't grab the drill yourself to perform the procedure on yourself. And in exercising our faith, whether it's in the flight crew, or the dentist, it's not necessary for us to understand the dynamics or the laws of aeronautics, nor is it necessary that we understand the science of dentistry, in order to put our faith in these things.
We should not be congratulated for our faith, as in, "My, but you have tremendous faith." No. The one who deserves our congratulations is the object of our faith -- the flight crew on the airline, the dentist, or, when it comes to our eternal destiny, God.
My read of scriptures is that we cannot save ourselves. We need help to get "from point A to point B," in terms of an eternal destination. We are not saved by our good works. We are not saved by our efforts. God is the author of salvation: he saw the need and satisfied it.
How do we actualize or realize the work on our behalf of the airline crew? By faith, we sit on the plane, and allow them to do for us what we cannot do ourselves (we let them fly the plane). How do we actualize or realize the work on our behalf of the dentist? By faith, we sit in the dentist chair, and allow him or her to drill our teeth and fill the cavity. How do we actualize or realize the work that God does on our behalf to save us, or grant us salvation? By faith, we rest in God's provision through Jesus Christ, and allow His plan to secure our eternal destiny.
Our faith does not save us. God does. Faith is only that disposition of the heart which allows God to do for us what we can never do for ourselves: provide for our own salvation.
In this sense, faith is different than belief because whereas belief can only be an intellectual exercise, faith actually has a practical outworking. I can understand and believe with my mind that the pilot can fly the plane and get me from, say, San Francisco to New York, but if all I hold is an intellectual belief, I will never get from SF to NY -- for that, I have to exercise FAITH by actually getting on the plane, and by actually putting my life and trust in the flight crew to get me to where they are going. Similarly, I can believe that God is capable of saving me, but I can only actuate His saving grace by putting my faith in Him and His plan and actually "getting on board," so to speak. One (belief) is an intellectual exercise only; the other is tantamont to an action whereby I actually benefit from putting my faith in the other party to do for me what I cannot do for myself. Again, the importance is the focus of our faith: in the Christian's case, the focus is Jesus Christ. Faith only actuates for me personally what Christ accomplished on my behalf.
In terms of worship....Paul says in Romans 12:1-2, "I urge you, therefore, brethren, by the mercies of God, to present your bodies as a living and holy sacrifice, acceptable to God, which is your spiritual service of worship...." My understanding of worship is simply this: allowing myself to be open to God for His use, a vessel for His Spirit to work whatever He wills through me, both to people in my life, and in circumstances I am placed in. I believe that this is the principal purpose of our salvation: that the union lost between God and man at the fall (in the garden) would be reestablished, so that God would be able to once again show Himself through people who have reestablished that union through faith....Not that they see me, but that they see Christ in me (Gal. 2:20). This is my hope. Worship is placing ourselves in a position before God in which He is able to live through us, for His glory, for His kingdom, and for those who come in contact with us in our lives. It's as simple as that. I don't consider worship to necessarily be that activity that takes place within the four walls of a church for a couple of hours every Sunday morning; worship is not "Sing a couple of songs, and listen to a sermon". Worship is the disposition of faith which places ourselves at God's disposal so that He can work out His will through us, and to others. That's worship.