You cannot gauge the behavior of a person in jail. Everyone reacts differently in a way. Jail is a high stress environment and people need to relieve the stress somehow. Some laugh, some cry, some scream and yell, some masturbate obsessively. It just depends on the person.
Crazy people are known to laugh at weird things. Things that no of us consider to be funny. But a crazy person in jail laughing does not in any way mean that he is 'happy'. It could mean anything, but most likely it is a reaction to stress. Especially if his crazy brain is finally starting to comprehend what is in store for him for the rest of his entire life.
That's a very keen observation, some people have guilt trips over little things, relatively speaking. You rush by people, you look rude, don't open the door for someone, something like this. I can't imagine having the weight of guilt of doing something like what he did.
I've even known of mainly, people who have killed others in drunk driving accidents (or not even necessarily drunk), an example, a guy in high school, I never knew the guy directly or personally. He was driving, he wrecked his car, a fellow student who again, I knew of, got killed. I believe the driver was hurt as well. Then, one of the last school assemblies of the year, 3 months or so after the accident, the driver of that accident that killed another student showed up. I was like, "you show your face around here?" Any of us can get into an accident that kills another person, fingers crossed but I could hardly bear that kind of weight of having done such a thing. The guy mentioned must have been out on bail, I'm pretty sure he faced, at least manslaughter. I still remember the names, the details, not so much. That was before the internet.
Like you said, it could be a form of relief. It may be a total disconnect from reality.