For some reason the router has a problem with my iPhone
Can you be more specific on what the problem between your iPhone and Router is? Your numbers indicate your iPhone is contacting your router, successfully negotiating a DHCP lease, and is using your router as an internet gateway.
I had an iPhone that was connecting to my WiFi network but was unable to access the internet when connected via WiFi. I went through pretty much all the steps you have performed and ended up going to the Genius Desk at my local Apple Store. They fixed the problem by replacing the iPhone, but neither they nor I had, or have, any idea why it would not connect.
