Can not open settings of xbox 360 on my PC.

Whenever I open xbox.com and click on xbox settings then it redirects me to this site.

https://support.xbox.com/xbox-one/security/error-child-trying-to-access-settings

Please tell what to do.

Because you can't edit parental settings on the website

That is ONLY for xbox one child accounts

But on my Xbox my privacy setting is marked as an adult.

If the browser on xbox 360 can not open a page you will need to open it on a PC or mobile phone that can.

You can not upgrade the internet explorer built into xbox 360 in any way.

Hmmm. Do you have access to the router GUI? Can you check the IP on your PC and XBOX themselves? On a PC open up a command prompt and type ipconfig, then scroll up to see what IP is on the interface. On the 360, you can check from System, Settings, Network.

Buddy, do you know if your NAT type is open?

You can double check this on both Xbox and PC
Xbox: Open Settings > General > Network config

PC: Open the Xbox Console Companion app > Settings > Network

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We can try isolating even more the issue, could you try share mobile data via wifi Hotspot and connect both Xbox and PC to the same Hotspot and give it a new try?