After I pay the 110$ to turbo tax my taxes will be filed?

Just paying the fees does not file the return.  You have to continue on and  go all the way through the File tab, through the 3 steps and hit the big orange Transmit Returns Now button.  

When you efile you get back 2 emails.  The first email only confirms the transmission.  The second email says if the IRS (or state) Accepted or Rejected your efile.  Accepted only means they accepted your return FOR Processing.  Not that your return is right.

How to Efile

https://ttlc.intuit.com/community/e-file/help/how-do-i-e-file-my-personal-individual-tax-return/00/25891

Paying the TurboTax account fees does not file your tax return.

You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the large Orange button labeled "Transmit my returns now".

After completing the File section and e-filing your tax return you will receive two emails from TurboTax. The first email when your tax return was transmitted and the second email when the tax return has either been accepted or rejected.

Your stimulus payment will be paid by the IRS either by direct deposit or by check mailed to the address on file for either your 2018 or 2019 federal tax return.