I'm also a single father whose kids live with him due to their mother's addiction problems. Welcome!
The approach I took with my children is that I tell them the truth but not all of it, and what I do say I say in an age-appropriate way. As my children have got older I've told them a bit more.
They know that sometimes their mum is ok and other times she's not but that it was not their fault and not their problem to try to fix. When they were young then that was more-or-less where I left it. When she's ok then they get to see her and when she's not they don't.
As they got older then I started talking to them more about alcohol and how it affects some people. A couple more years and I talked to them about addictions and why it's so hard for their mum to stop drinking and, most importantly from their point of view, stay stopped.
All through this I have repeatedly said that they need to remember that their mother's problems are not their fault. Children have a big tendency to assume that it one or other of their parents is unhappy / angry / out of control / whatever then that is somehow because of something the child did. It is crucial for children of people with addiction problems to realise that it's nothing to do with the child and that the child can't make the addicted parent not drink/take drugs. And that's regardless of what the addict might say ("If only you got to see me more often I wouldn't need to drink!" 
). A parent's addictions are nothing personal against the child and the child needs to be repeatedly reminded of that.
As well as talking to them I do my best to listen to them as well and do what I can to validate their feelings. It's ok for them to feel angry. It's ok to feel sad. It's ok for them to go out and have a good time even though their mum has drunk herself incoherent again. It's ok for them to feel angry with me, too - but no matter how angry they are with me, no matter how hard they try to push me away, I make sure they know that I'm going nowhere and that I will always be there for them.
My son doesn't talk much about his mother at all but he does sometimes. My daughter is much more willing to talk about her feelings about her mum and I notice that my son is usually listening in closely even though he won't say much. I also tell stories about their mum about stuff that's nothing to do with her drinking - things we did and places we all went to when they were tiny, how their mum and I met, all those sorts of happy memories. I think that's important. I don't want them to think that any conversation with me about their mum is going to be a downer. I don't want them to think that I have nothing positive to say about her. She is their mum, after all.
A big part of the problem my children have with their mother is their feelings about her letting them down when she chooses to drink rather than to be able to see them. So I try really hard to make sure that they feel that even though they can't depend on her, they can depend on me. I am scrupulous about not making promises to them that I can't keep. They don't always feel safe around her so I make really sure that they can always feel safe around me. I don't drink much these days any way but I'm always very careful not to be drunk when they're around.
I wouldn't show your son the court documents, not for a long time. I think they will be too cold, clinical and explicit. But there must have been incidents when he was in his mum's care when she was so out of it that she behaved inappropriately and wildly inconsistently. Maybe pick a time when he's not angry at you and ask him about what he remembers. He may say nothing for fear of being disloyal to his mother. That's ok. If he does tell you something that happened that you weren't aware of, try really hard not to get angry no matter how bad the situation was. He needs to feel safe to tell you this kind of thing.
One final thing - take opportunities to look after yourself, too. Accept help from those who offer it. Ask for help when you need it. Being a single parent can be hard work even without the extra crap thrown in to the mix caused by having to deal with an ex who has addiction problems. I love my children dearly but I do really benefit from having some time to myself when I can.