This is a very awesome very long post!
When I start explaining my interests to someone, I tend to get incredibly focused on them and jump between different areas of the topic (which can be hard to follow) but it also means my family has to live with the fact that if I start talking about something in detail, they're going to be there for a while. (That may just be regular old infodumping though.)I also end up in a flow state when doing maths a lot of the time! (I'm fairly good at it)
I have no clue what my IQ is. I'm not great at pattern recognition in images though (I can do numbers)