Sony Xperia Z1 Compact User Manual

Have you tried using your headphones to other devices? If it also doesn't work to other devices, then you have a faulty headphones. If that's a new headphones, then you can get a replacement.

Check if there's anything on the headphone jack that may be blocking the connection. Have you tried using a different headphone to your phone?

I want to listen music with my Sony Xperia z1 with my headphones is not working, what can I do

Yes I tried the headphone with and other devices it work good

Hi Ester. Does it show any notification or window with a message about this? When you dial a number, do you hear a ring or not? Please provide these info so I can help you out. One more thing, check if you still have enough credits to make a call.

I have the same problem right now so i came to here, hope to find a solution to that drop

You can, but you need to install a widget for that. Something like World Clock & Widget (link) from the Google Play store should do what you're looking for.