You apparently misunderstood how you could pay your federal taxes. There is no way to apply a state refund to taxes owed on a federal return. You can use direct pay: <a rel="nofollow" target="_blank" href="
https://www.irs.gov/payments/direct-pay">https://www.irs.gov/payments/direct-pay</a>
Yes there will be a penalty and interest for late payment. The IRS will bill you for the amount of penalty and interest.
