How do they know when God is angry?

[Angrboda]

Can you demonstrate that djinns exist apart from your book?

Sure. 
They are around us, they live with us but it is kinda they are in a parallel universe (whose coordinates exactly the same with us).
They see us, we can't see them (Araf 27).
They normally only can whisper ideas in our minds (sometimes we really think those ideas are ours) but actually they are from them. 
However, under some circumstances, they touch our lives physically.
The main reason for it is black magic. Some people (generally people with innate or acquired abilities to communicate them) make dark agreements with them. And use their abilities to harm you.
You can see tons of videos in Mr. Ballens (not a religious man at all) channel about people who are suffering from those experiences.

First, people having certain ideas in their mind is not evidence that those ideas came from djinn, or even that they came from anywhere but the person's mind.

I'm not sure what you are claiming about MrBallen's videos. Could you be more specific -- his channel seems filled with an odd grab bag of remarkable stories. I'll tell you in advance, however, that people claiming supernatural experiences is very poor evidence for those supernatural things as we know that many times people are wrong or mistaken about such experience.

I'm not seeing much at all of a demonstration of their existence. I have as much reason to believe in Thor and his hammer based upon evidence of this low quality.