These are valid questions for atheists to ask. Even believers have questioned God at one point in their spiritual walk; If they haven't, they're lying because as a believer, the Bible says you will have trouble in this world. Since believers aren't exempt from trials in life, it can lead them to question their faith especially if the trials are back to back. I want to elaborate on Questions 1, 3 & 4.
#1. God never intended the world to be ridden with suffering and evil, but because of Adam & Eve's disobedience, sin entered the landscape, and we see the evidence of that today. Another example is when Lucifer (originally one of the angels of Heaven) tried to assert himself above God, and God ended up banishing him and 2/3rds of the angels to hell. Adam & Eve were supposed to have dominion over Earth, and they gave dominion to Satan when they disobeyed God. What's going on today is a reflection of sin.
#3. I believe if you do wrong, YOU should face judgment. Everyone shouldn't suffer for one person's disobedience. If I was God, I would spare everyone from Adam & Eve's judgment. In other words, Adam & Eve would pay for their disobedience, everyone that comes after them would be exempt. While sin is a condition, the choice to sin falls on the person. God gives us free will to do right or wrong.
#4. I shake my head at Christians who do evil. Christians who do evil are NOT my brothers and sisters in Christ because they make me look bad. One person/a few people can mess it up for everyone, and Christianity is no different. When unsaved people see Christians doing evil, they label all Christians as foul based on the actions of a few. For believers, YOU may be the only Jesus someone will ever see, so it's important to represent Christ well. That doesn't mean fronting like a perfect Christian, it simply means keeping it real. Too many Christians front like they're holy & sanctified, and when they're exposed, they deny. One thing about me: I'm a believer, but I foul up from time to time like everyone else. I own my mistakes, and keep it moving.