Can the law firm charge interest if it claims attorney fees?

No

According to the lawyer's charging standards, the lawyer charges based on the subject matter. Because lawyer charging standards vary across provinces and regions, you need to consult your local law firm for details. In addition, the fees for administrative cases, criminal cases, and economic disputes are also different. If it is an administrative case, the fees will be based on the subject matter. If it is a financial dispute, the charges will be based on the subject matter. So no interest is charged.