Life always has a way of playing out things it's own way regardless of how we plan or what beliefs we have. Personally, i don't think God has a hand in any type of ill faith that befalls different people. I mean, his a merciful God, he can't let people suffer.
Believing that God punishes people is almost not conceivable to everyone because not everybody believes in God, and those who believe, have different thoughts on how God works. Drawing from this, i'll like to make an argument or a statement to be precise.
How about those who do not believe in God and lead a meaningful life, if bad faith befalls them, do they say it's God? Who do they blame for any suffering they go through? How do they call it punishment? Plus they are other people who start to suffer from the very moment they came into this world. Surely God won't do that to innocent children for they haven't even seen life itself.
Secondly, if God does punish people, it will be because they fail to do the one thing he asked of us, worship him and lead a meaning life in a righteous manner. Now, i know tens of people who do not measure up to the standards expected of us by God. Some of these people do not even think about God talk much of worshipping. And yet, they live a painless life with all the fine things money can buy. They've never for once suffered in their entire life. How do we explain this inline with God punishing people?
On the subject of whether Satan has the ability to punish people or not, my stands is that Satan can only do to us what God gave him the permission to do, correct me if am wrong. I think Satan gets too many blames. His role in this world is to distract us from worshipping God as he said he would show God when he refused to bow before Adam and Eve and not the many things we often blame on him.
In general, i think suffering is just a part of life. And there are things that no matter how much you try and even pray about it, It never gets to change, otherwise we wont have too many religiously devoted people suffering on a daily basis. My point is God has no hand in most of bad faith a lot of people go through and that includes suffering. He might only be responsible for certain punishments if you test him directly.