It should be accessible by logging into your turbotax account online and checking progress on your current taxes. Using these programs does make one feel quite removed from what's actually happening. I believe it is possible for money owed to state to be paid with funds from a federal return. My memory is a little fuzzy on the issue, but I believe I've experienced exactly that some years ago. Just check out the status of your state tax return. I believe you'll find that it's all taken care of based on my understanding of your situation. Do feel free to reach out to tech support if you're still worried, as I'm just a fellow turbotax user.
Taxes owed can Never be deducted from a tax refund, federal or state.
What you are seeing is the Net of your tax refund and does not in any way mean your taxes owed have been paid from your tax refund.
If you selected to pay the taxes owed by check then you should print the payment voucher and mail the voucher and check to the address printed on the payment voucher.
No, you cannot pay your state taxes with your federal refund. You can look at your states website for payment options.
Please see What are my options for getting my state refund or for paying any state taxes I owe?