I suggest that the most natural way to say it is: "The Internet connection is down and I have to stop doing my homework." We refer to a singular internet connection, not connections. We would say to call a halt TO doing something. "I'm calling a halt to doing my homework." People refer to the internet being down, or broken, or maybe not working. "I have to call a halt" is not the natural, common, way to say it. Halt is a very formal word. We would normally say "I have to stop."

I mostly agree with Robert. Halt is very formal and can sound a little agressive or an imperative. You might hear military people use it as a command. Stop is much better. But I would modify the sentence slightly to make it sound more natural (although Robert and Nate are closer to what you have said). I think the most natural sentence would be; "I can't do my homework because the internet is down' (you could swap 'down' for 'not running' 'broken' or 'not functioning') If you wanted to use 'Call a halt'. It would be more likely used if you were in some kind of position of authority over a project of some kind. For example; "The risks are just too high! I am calling a halt to this project, right now!"

Thank you so much!

If the issue is current, we would commonly say, "The internet connection isn't working, and I have to stop doing my homework." or if you are insistent on your wording. "The internet connection isn't running properly, and I have to place a halt on my homework."