Is it permissible to establish a fast-food restaurant—such as one serving chapati—where customers typically eat in the street, given that there is mixing between young men and women when purchasing?

There is no objection to opening a restaurant where permissible foods are served, but unlawful mixing must be avoided by allocating a place for women and another for men. If avoiding mixing is not possible, then it is better for a Muslim to avoid this work and seek another; due to the Almighty's saying: ﴿And whoever fears Allah – He will make for him from his matter ease. And will provide for him from where he does not expect.﴾, and the Prophet, peace and blessings be upon him, said: "You will not abandon anything for the sake of Allah, the Mighty and Exalted, except that Allah will give you something better than it."