how does google chromes incognito thing work?

Chrome Incognito is a temporary session where you can browse the web without history being recorded on your computer. So when you exit it, nothing is left behind from the browsing. That should clear about incognito mode.

In the end, your dad will still be able to track the websites/searches you visit on the router. Since the router logs the IP address connections on it's own internal memory. Something that incognito has no control over.

If you want to not be tracked like that, I suggest you use proxy websites or proxy software. It'll mess with the IP address connections so your dad won't be able to pinpoint what you visit.

When you close an incognito window its like it was never there. Nothing shows up in history and google doesnt show any recent searches. I use it when I don't want others to see my business.

When you search something in google it doesn't show up in your history