Yes. They loaned you the money, and if the account is closed it simply means they will not be willing to loan you anymore now or in the future. But, what they have loaned you must be paid back and with interest/late fees if they apply.
Unfortunately yes, and it will continue to accrue interest until you work out a reduced interest plan with them or until it is charged off and/or sold to a CA. I suggest calling them and trying to work out a payment plan with lower interest. No guarantee they'll agree to it, but it's worth a shot.
