Question number one:
Is Ivan in a prison?
I think that he is. Mainly because, he has inmates, he has a time to wake up. And last, there are punishments.
An example of a punishment was when the warden informs him that Shukhov—identified officially as prisoner “Shcha-854”—will be punished for not getting up at the proper time. He says that Shukhov’s sentence will be three days in the hole.
If he is in a prison, what did he do to get there?
I have no idea of how he got there. There are many options, slavery, robbery, ect...
Question 3: Why doesn't Ivan (warden) throw people into the hole? Has something happened to him when he was younger?
Well, Children are sponges, after all we all know this. And there’s a small but intriguing body of evidence suggesting that beyond a child’s disposition, a parent’s stress level can affect a child’s very makeup, including his or her risk of mood disorders, addiction, and even disorders like ADHD and autism.
So maybe something tragic happened when Ivan was younger. Just like we studied in humanities class. For example: Someone almost died because of an airplane. The person will get scared of airplanes and will never ride them again. So that leads me to think of Ivan's past, when he was young. Like really young. Did he loose his father? Was he treated well? How connected was Ivan to his family?