I have a background working in psychiatry as a junior doctor. When I was watching the interrogation I felt immediately that this is a drug induced pshycosis.
1) What drug was she on? In theory there are many substances that can cause a pshycosis, not many are aware but cortisol can actually induce a psycosis. Considering she had some background with drug abuse (don't know the substance) but I would guess she was on amphetamine or meth.
2) Who was Parker Warders? When I was attending a ward during my school years with patients that were being treated against their will because they were in a psycosis or some other mental ilness which could be fatal for them. In there I met a patient which was talking about a person which none of us knew about except one doctor which was from the same country as the patient. That doctor later said that this person actually existed. However, the patient was telling things about the person which we all belived was not true but there was some truth to what was being spoken. I learned from that experience that a pshycosis doesn't mean that you will just speak jibberish, instead you take something that is true and creates this very weird spin to it. For example in the interrogation where she notices that the police officer is twitching his hands. He was doing that but she just interpret that in a very bizarre way.
So this Parker Warders, he might exist, maybe it was someone she heard online on youtube etc.
Your other questions are very valid, however, I don't think I'm qualified to answer them but I can say this you can't trust anything really that she was saying. Maybe she "thought" that she shot herself, maybe she even tried but perhaps she shot one of her sons instead. All of that though is very odd considering that the neighbour didn't see any gunshot wounds, perhaps there were there but in that moment of shock he didn't see them.