I think kaylee2850 gave some good advice but I see it a little different. I don't believe you can compare cases of PTSD. The one constant is the effects, such as anxiety, anger, depression, etc. What may be traumatic to one person might not be all that traumatic to another. The cause of PTSD is what is different and it can be any event that one takes as traumatic. For instance, I've been diagnosed with PTSD and a sudden loud noise really gets to me. My friend also has PTSD and noise doesn't bother him but violence does.... on the other hand, violence doesn't really bother me.
So it is different in those regards and absolutely someone can pick up PTSD by living with someone with PTSD.
He could have got PTSD if his dad caused really traumatic events in his life to where he would get it, but more than likely if he has PTSD he would also have flashbacks with it. He could just be suffering from the ADHD and anger issues or just trauma. PTSD isn't something easy to get I mean it would have to be such a traumatic event that it would ruin his whole life to the point he feels like he's always re-living it whether it be from flashbacks or literally. I've been diagnosed with PTSD, anxiety, trauma, and depression for years now. And I have it so bad it's equivalent to someone who's been in the military for 20 years. The only way you will truly know if he has it is if he goes to a therapist or counseling and actually opens himself up and tells them everything. He needs to want the help to get the help.
I have cousins that have schizophrenia like me it could be hereditary depending on the trauma invovled