Is our dignity encased in God's dignity? Do we disrespect Him when we disrespect one another?
Yes. We disrespect God when we disrespect each other, because God is our creator. Just as we would disrespect the artist of a painting by flinging mud at that painting, we can also disrespect God in the same way. Furthermore, God created us to be saints, and to spend eternity in Heaven with Him. (Whether we actually do that or not is, of course, our own choice.) But since we were created by God, loved by God enough for Him to give His life for us, and so forth, we are not on a level with the animals. We are loved by Him, and when we disrespect, wrong or hurt each other, we are doing those things to something (or someone) that God loves, and has loved enough to die on the Cross for. I'm sure there are lots of implications of disrespect and ingratitude there, to say nothing of disobedience to the law of God, that we should love one another, and do good to even our enemies.
Does the 4th commandment come under this? Must we respect only our own parents and authorities or all elders?
We should respect all human beings in one sense or another. Granted, of course, that those in authority over us deserve a special kind of respect for their office and authority, even if they themselves are rotten, horrible people. (Because the authority comes from God and is God's, even if the person carrying it is rotten.) When we disrespect those in authority over us, we disrespect the authority God has given them. Elders, I think, should be respected for their seniority and wisdom, but also we must remember that we need to have a respect for every human being because of what they are (a creature of God, and a soul God loves), and because God has commanded it.
By the law of charity, we are NOT commanded to simply be abused by everybody. But there are cases in which we ought to bear even abuse, because the person has authority, and we must respect their office. (Eg, we must "turn the other cheek" sometimes.) In terms of everyone in general, we should obviously try to preserve ourselves from being abused or mistreated... however we are not given the right to seek revenge, to lash back at people, or to mistreat them in return. Walking away so someone doesn't verbally abuse you is one thing. Sinking to their level and bashing them back is NOT acceptable. Walking away, even if it means "being rude" by ignoring them, is simply you trying not to violate the law of charity. Bashing them back is you breaking that law.
We must learn to think of souls as the saints thought of them... creatures of God which Our Lord loved enough to suffer and die in order to save. If we contemplate the love He bears for each one of us, and the desire with which He desired for us to be saved, we realize quickly how it will look to Him if we, on the other hand, see nothing wrong with disrespecting or mistreating those souls He loved so dearly.
Words were attributed to Our Lord, to the effect of "If only each soul knew how much I love them. If only they knew EACH soul is My favorite." (Anyone with "I Wait For You" can correct the quote if it's wrong.) But we need to understand this fact about God... that no matter how rotten people may be, GOD loves them. He wants them to be saved, even if we are tempted to hate and despise them. But if we cultivate in ourselves a true and deep love of God, then it becomes ever more impossible for us to hate or despise anyone, because in time, we realize that God loves them, how MUCH God loves them, and we cannot bring ourselves any longer to hate what God loves. This is true love, both of God and neighbor... to love ALL men, because God loves them, and to desire good for them, and above all, their eternal salvation. To do good to all men as much as we can (and as much as is prudent), and to pray for all men.
Understanding the love God has for each of us, and loving Him so much that we cannot help but love what He loves, is the key. That is what real charity is all about.