Say If I got approved for a 0% apr for 12 months credit card with no annual fees and I used the card and paid the balance off on lets just say the 9th month so when the 13th month comes will I have a bill due if I haven't made any charges on it sense the 9th month when it was paid off?
The credit card company will probably send you a bill statement every month, whether you use the card or not, even if you don't owe them anything. Are you planning to keep the card after you pay it off and the 12 months of no interest ends?
If the card has no interest for 12 months, why would you pay it off in 9 months? Why not wait until the 11th month to pay off the balance?
You will receive a monthly bill regardless of your balance. If you follow the terms of the introductory offer to the letter, your balance at the end of the introductory offer will be zero.
Keep your eyes on that contract though. Many of them keep track on the interest you would have been charged. If you're one day late they may be able to charge you all the back interest.
And study how to properly use a credit card without paying interest as well.