Thank you for your response and for the insights! It's good to hear some real-life challenges because sometimes I think this is too much of an utopia-like idea. I hope that you overcame those struggles and that those had made your work only stronger afterwards.
This idea of mine definitely needs some good thinking through.
It does include the possibility of hiring homeless people and paying them a fair wage (while others would volunteer), and one of the solutions might be to start symbolically charging for food from the beginning to make it sustainable. And of course, the amount of donated food has to be taken with a special care in order to have enough for everyone.