Why do great things happen to unbelievers and even bad people?
In Church there is talk about blessings of the Lord for those who love Him, etc.
But what about those that are blessed that don't love him? How does that work?
You could take the word "atheist" here and replace it with any group. Any religion, including (yes, really) Christian has people who fit that description. And there are people from every religion, and atheists, who that description fails to describe. You could also use labels such as political alignment, county of origin, gender - and you'd get the same hits and misses.
I believe you are very deeply confused about the relationship between what people believe (in terms of religion), and how people act, and whether they are successful / constructive / whatever. And I have no idea how "good looking" plays into this question!
But: if the question is "why don't atheists live according to Christian teachings"... Er, because they don't believe them. I could equally ask "Why don't Christians live according to the teachings of Hindu/Islam/Zoroastrianism/Norse-Mythology?".
Re "living by different rules"; you may be aware of something in your location called "local/national/international law". Most people live according to their society's laws, which are usually based along the lines of "don't harm eachother" - do not steal, do not kill, etc (aside: please don't think this means these laws come from the Bible; these same laws have evolved in every successful culture, including those completely separated from the Bible; it seems such laws, and things with health implications ("don't eat each other", "having kids with your sister is not a good idea") are a pre-requisite, for self-evident reasons, for a successful culture). As it happens, this is often fairly compatible with many religions. Indeed, there are many laws in the Bible that are largely disregarded even by believers (most Christians in Western cultures are happy to use contraception, for example (citation: Catholicism). A reasonable case could be made that many Christians are primarily also following the society law, rather than Biblical law.
Finally, Christianity does not, AFAIK, claim to make you rich, healthy, successful or attractive. Any claims of such are usually limited to the afterlife. Which is convenient.
I'm not entirely sure what the question is, but hopefully I've touched on some of it?
The problem of theodicy is present throughout the Bible, and so I am not going to give an exhaustive answer. I will say, However, that even Jesus said that His Father caused "rain to fall on the just and the unjust alike," (Matthew 5:45)), meaning that in this present age, the wicked will, in fact, be seen to prosper.
Some of what the Bible says on the matter can be found here.
One of the better answers to theodicy is to remember that God is both just and merciful. A formulation that is used throughout the old testament is that God is "slow to anger, but abounding in mercy.". That God would give the wicked every chance to repent is in His nature, and a blessing for all sinners who choose to repent.
To your point that the wicked must be punished in order for Chrisianity to mean anything, well, May I suggest Jesus has a story you need to hear?
One of the most famous parables - called alternately the parable of the Produgal Son or the Parable of the Loving Father, is completely against the idea that the righteous should expect or take any solace in the punishment of the wicked. After the Prodigal returns, the older brother is, to put it mildly, pissed. After all, why should the young brother be forgiven? When the Father takes the older brother aside, he encourages the older brother to rejoice in the return, not worry about the evil that has been done.
It is against the Pharisees this parable is directed. the story is a picture of God's loving response towards sinners, and a warning against the righteous not to be annoyed that repenting sinners are received with open arms.
In short, as a sinner myself, I am to rejoice at God's forbearance. I regularly praise God that I didn't get "what I deserve.".
But, as Galatians says, do not be deceived, God is not mocked. What a man sows, so shall he reap.
In short- God loves all people- (even the guy trolling on this site saying he'd raped my mother!); that does not mean he loves their sins. I also believe (and this is one area of thought that is open to dispute) that God=joy and thereby all who truly seek joy, whether in this life or in the next, will be redeemed. This makes me a Universalist but I am not entirely alone in that belief. Seeking God means seeking the light.