Is it permissible for a student studying in the West to work for a company that operates a unified network of retail stores selling prohibited items such as alcohol and unlawful meats, given that all banks deal with usury and it is impossible to avoid interacting with them?

If the student's work in the company is permissible and has no relation to what is forbidden or assisting in it, then there is no harm in it. And connecting a unified network for stores to enhance their competitiveness is acceptable, and the presence of some violations in those stores does not affect it, as long as they are not dominant and intentional.

A Muslim should fear Allah and seek what is lawful in their earnings and food, because unlawful gain hardens the heart, removes blessings, and prevents prayers from being answered.

As for dealing with usurious banks due to the necessity of no Islamic banks being available, it is permissible only to the extent of need, such as opening a current account while leaving the least possible amount of money in it.