My knowledge of these questions has changed over the years as my understanding of law and mercy has grown. Chances are, they will still improve and my understanding is still only a portion of a bigger picture.
I used to think that Christ suffered because Satan and his kingdom was wailing on Him. Much like Joseph Smith in the grove when he was attacked and thought he would die. This view changed with a single scripture.
D&C 88
I changed my perspective immediately and realized the suffering Christ endured was from His Father. Seems like a weird relationship and almost abusive but as I pondered on it I realized a few important points.
(Did a quick search for an image of "the wrath of God" and this came up. Thought it pretty funny.)
1) The wrath of God is infinitely greater than the wrath of Satan. God being all powerful and all knowing downplays anyone else to give suffering. Especially if it is to be incomprehensible to anyone who has not experienced it, I wonder who else could it be from?
2) God the Father is the only person from whom the punishments of His laws could come from. (Read my previous post on Law, Justice, and Mercy) Because the blessing for the laws of the Father are Eternal Life and nothing short of it (There is no Law from the Father that gives a lesser blessing (As far as I know and from what I understand the Father cannot make laws with less of a blessing or it is not a perfect law and He would not be a perfect God. Could be wrong here but it is my current understanding), then the punishments for breaking those laws are eternal punishments, or God's punishments. Meaning, God is the one who has the power to give eternal life and equally so, eternal punishment.
3) The atonement is given so much definition in how it helps everyone and everything. Have we considered what it did for Christ? We know it helped him succor his people (Alma 7:12). We also know that when it is done Christ can finally say, "I have overcome all things and have trodden the winepress alone." (D&C 76:106-107, D&C 88:106) If Christ has overcome all things, then He is like his Father, all powerful. He has gained the love and power needed to act as His Father does. If he did not suffer the wrath of his Father, this could not be.

Here is where it gets tricky. What is the opposite of God the Father? Nothing right? Some might be thinking of Lehi's discourse on opposition but his sermon is about opposition not opposites. Even God the Father has opposition to His work. Just no opposing power that matches His own. Now what of Christ? Well, He has overcome all things, meaning there is no power in existence that can overcome Him. He is eternal then. Anything that has no opposite is eternal. The atonement made Christ Eternal.
I learned the Savior suffered the wrath of an Eternal God, that Christ overcame that and is now Eternal and has the power to raise us up, cleanse us, and bless us. These answer the first two questions for me. Now what does this mean to me?
It means, I don't think I could overcome that and so I don't want to suffer that. I better follow Christ and keep to the plan of mercy and forgiveness. I also realize my personal sufferings can help me better succor others but also get to know my Father and His Son. I should not shrink from a hard task like looking bad when apologizing to others I may have offended or sticking my neck out for those who may be despised of those around me. I should be willing to give even my position in babylon to help others and bring them to this same knowledge, the Christ lives though he died, suffered the wrath of God so we don't have to, and gives us a path to follow to receive the blessings of eternal life that were otherwise lost to us. Nothing could be more important.
I learned the Savior suffered the wrath of an Eternal God, that Christ overcame that and is now Eternal and has the power to raise us up, cleanse us, and bless us. These answer the first two questions for me. Now what does this mean to me?
It means, I don't think I could overcome that and so I don't want to suffer that. I better follow Christ and keep to the plan of mercy and forgiveness. I also realize my personal sufferings can help me better succor others but also get to know my Father and His Son. I should not shrink from a hard task like looking bad when apologizing to others I may have offended or sticking my neck out for those who may be despised of those around me. I should be willing to give even my position in babylon to help others and bring them to this same knowledge, the Christ lives though he died, suffered the wrath of God so we don't have to, and gives us a path to follow to receive the blessings of eternal life that were otherwise lost to us. Nothing could be more important.