Try another Wi-Fi router.

Is this something that is covered by o2?
Is the router part of the contract I have with o2?
To make an example: when I end the contract, should I ship the router back to o2? Because in that case, I would expect o2 to provide me a fully functional router

I don’t know what router you are using and I don’t know if you rented it from o2 and I don’t know whether your router is defective. 

Yes, it is the Homebox 6441 provided by o2.

And I have no idea if it is defective (looks so), and if i rented. I just submitted my contract to the legal office of my employer to see if I can receive some support from them.

I tried to call the support line from o2 so far with no luck, and this is really damaging my work

Hi @sr.richie 

Welcome to our o2 community. 

Do you know our o2 my service app? The app can support you in case of problems with the DSL and WiFi connection:
You can switch to english language via app settings after the installation.  
Then you can use the app to check your DSL connection for errors.
If the app cannot fix the error, it generates a process number,
with which you can then report to the DSL fault hotline,
where the colleagues will create an error ticket with you to check your connection.

Best Regards.

Matze