1. I think it is precisely what you said. Having the attitude that "God, I want to do anything you say, and I give all to you, because you are the only one worthy enough and wise enough to run my life. I trust you with everything I have and all that I am... I surrender it all to you" This is what it means to "believe on the Lord Jesus". The bible is very clear that it is by faith that we are saved. It is also very clear that that faith is inseparable from works. This is because you cant separate trust with obedience! If you say you trust someone, and do the opposite of what they say, you prove by your actions that you dont believe in them. Being saved is giving your life and everything you have to God because you believe in Him, because you trust Him with all that you have. True faith, repentance and works are totally inseparable. You can have a false works that arent done out of faith, and this is religion. And you can have a false faith that doesnt include works, and this is Antinomianism.
2. I believe when you put them in context these sciptures are more than clear and speak for themselves.
Colossians 1:21-23 And you, that were sometime alienated and enemies in your mind by wicked works, yet now hath he reconciled In the body of his flesh through death, to present you holy and unblameable and unreproveable in his sight: [u][b]If[/b] ye continue in the faith grounded and settled, and be not moved away from the hope of the gospel[/u], which ye have heard, and which was preached to every creature which is under heaven; whereof I Paul am made a minister
2 Timothy 2:11-13 It is a faithful saying: For if we be dead with him, we shall also live with him: If we suffer, we shall also reign with him: if we deny him, he also will deny us: If we believe not, yet he abideth faithful: he cannot deny himself.
Hebrews 10:24-31 And let us consider one another to provoke unto love and to good works: Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching. For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, But a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. He that despised Moses' law died without mercy under two or three witnesses: Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace? For we know him that hath said, Vengeance belongeth unto me, I will recompense, saith the Lord. And again, The Lord shall judge his people. It is a fearful thing to fall into the hands of the living God.
Hebrews 12:12-17 Wherefore lift up the hands which hang down, and the feeble knees; And make straight paths for your feet, lest that which is lame be turned out of the way; but let it rather be healed. Follow peace with all men, and holiness, without which no man shall see the Lord: Looking diligently lest any man fail of the grace of God; lest any root of bitterness springing up trouble you, and thereby many be defiled; [u]Lest there be any fornicator, or profane person, as Esau, who for one morsel of meat sold his birthright. For ye know how that afterward, when he would have inherited the blessing, he was rejected: for he found no place of repentance, though he sought it carefully with tears.[/u]
Romans 11:20-22 Well; because of unbelief they [the jews] were broken off, and thou standest by faith. Be not highminded, but fear: For if God spared not the natural branches, take heed lest he also spare not thee. Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.
John 15:1-6 I am the true vine, and my Father is the husbandman. Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit. Now ye are clean through the word which I have spoken unto you. Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me. I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing. If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned.