Q - 2 Peter 3 speaks of salvation on the day of judgment, and the importance of living a life of good works. How does this fit into salvation by Christ alone?
Answer - Peter makes clear that we have righteousness by faith (cf. 2 Peter 1:1), and he joins the chorus of other NT writers in affirming that someone born into God's family by faith will normally demonstrate their new birth by a life that honors God, a life that expresses good works (cf. Ephesians 2:10, Titus 2:14, James 2). While our "salvation" from sin's penalty is not conditioned on our good works, our good works are important to God, and will be the basis for a future evaluation re: faithfulness at the judgment seat of Christ (cf. 1 Corinthians 3)
Q - Can you put propitiation into a simple, child-like explanation?
Answer - I can attempt to! The basic idea is one of "satisfaction." Imagine this scenario: A neighbor who doesn't like to hear your new puppy barking decides to secretly put a treat with poison inside your pet's enclosure. The next morning, your beloved new pet lies dead, and you discover (because you had a camera "watching" your pet's enclosure) your neighbor is the culprit. You feel anger as your children cry and ask you "Why?" Would it satisfy your family simply to go on with life as if nothing happened? Not likely. No, justice demands that some penalty, and perhaps restitution, be enforced. Our sin requires a satisfactory penalty in the holy and just heart of God. And Jesus' death satisfied God's righteous wrath against the hurt and destruction the sin of the world's people has caused.
Does that help?
Q - Doesn't man DO something to earn salvation, namely, he needs to accept the sacrifice of Jesus or the offer goes unclaimed. Does this mean man does play a part in his own salvation?
Answer - The Bible clearly presents the need for man to respond to God's offer. Yet it never presents "faith" (or believing in, and accepting God's offer) as a meritorious work. It is simply receiving a gift, offered by love and grace, relying on God's solid promise secured in Christ. Man does not "play a part" in his salvation as if he could provide any part of it for himself, or earns any of it through any meritorious action. Grace offers the gift; faith receives the gift.
Q - Why couldn't God alone forgive our sins?
Answer - Actually, God alone is the only one who could forgive our sins, but not simply by saying, "Well, that's OK...you sinned, but there are really no consequences." He wants us to recognize how destructive sin is, so destructive that not only it ruins our lives, but it brought to death the life of a totally innocent person, the Lord Jesus Christ. Being thoroughly just, and as a Righteous Judge, God must exact a penalty for sin...or he would not be just. Because Christ died for us, Romans 3 says that God can be both "just" and the "justifier" of those who have faith in Christ.
Q - Do you think Christ's reason for dying on the cross was just his love for humanity, or did he do it to cleanse God's name and act on His attribute of justice?
Answer - Clearly, Christ's death in our place was motivated by His (and His Father's) deep love for human beings...for every person. It was also to satisfy God's righteous, just nature. No righteous judge can simply allow a guilty part to go free without paying for the wrong done. What kind of world would we live in without justice...there would be no "right" or "wrong." We would live in chaos. So Christ's death vindicated God's character, demonstrating his passion for right and righteousness and correcting what we have willfully destroyed through our sin.