This is inaccurate. The father started both the Korean War and the North Korean cult of personality. (the personality cult started in the 50's and 60's under Kim Il Sung) It became more outlandish under Kim Jong Il but it is at its core a Stalinesque personality cult.
https://en.wikipedia.org/wiki/North_Korean_cult_of_personality
As for why they build nukes this is a good article. Basically it's for the same reasons I told you before, Qaddafi and Saddam didn't have nukes and look what happened to them.
https://www.newyorker.com/magazine/2017/09/18/the-risk-of-nuclear-war-with-north-korea
I see no evidence of this. Their intentions have been extremely clear and consistent for decades now and I see no reason to believe they have changed. Nuclear weapons ensure regime survival in a way conventional weapons never could, especially if they have the ability to strike the US. We are far less likely to gamble with American lives than we are Japanese or Korean lives. It's common sense.
So why didn't Kim Jong Il start a war when he was dying? Or Kim Il Sung for that matter?