Will my automatic payments stop once I've paid my taxes? I don't want the IRS to debit more than I owe.

Yes, once the debt is paid in full the debits will stop. 

Once your taxes have been paid in full you will get a letter detailing the amount you paid.

Thank you!

Will the letter indicate that the arrangements has been fulfilled?  How long after final payment? 

I have automatic payments drafted from my bank account monthly.  It always comes out on the 15th of each month. It didn't come out this month on the 15th. That concerns me. 

Check your account at the IRS :  https://www.irs.gov/payments/view-your-tax-account

If you still have a balance due then check with your bank.