Is a person guilty of a crime if they don't realize they commit it?

In a legal sense, yes, but in a conscious sense, no.

Consider a baby taking something that belongs to someone because they like it and they have no concept of property rights, you wouldn't call the baby a criminal. The law still calls it theft... But surely the police would know better than to arrest the child.

Edit: Who gave me a thumbs down? you're just mad I stole something from you when I was a baby. I'm sorry, I didn't know better. No, you can't have it back. I ate it. I thought it was food.

There are crimes of commision, thing you do. Crimes of omission, things you don't do. And crimes of ignorance, things you should have known not to or to do. Basically any way you look at it you're screwed.

Legally, yes. Morally, don't feel guilty. It was just stupid.

Only if they are reckless, in action.

For example drinking to excess then getting into a fight..

yes