What is the ruling on working in customer service for a clothing company that sells some permissible and some impermissible items, given that my role is not limited to selling the impermissible clothing, and knowing that there is usury (riba) on debts that are not repaid within three months? Is the money earned from this work permissible (halal) or impermissible (haram)? And is it permissible for me to use it in a case of extreme necessity?

There is no objection to working for the company as long as the work itself is permissible, and you do not directly engage in or intentionally assist in anything forbidden. This includes providing customer service over the phone for purchasing clothes, even if they might be misused, as long as you do not know the buyer's condition or intention. The issue of usurious fines is not permissible, but there is no objection to the salary you receive, and the mixing of the company's money does not affect it, because when haram (definition) money mixes with halal (definition), the halal does not become haram.