MY RETURN IS IN PENDING—what does that mean?

Did you e-file?  Did you click that big orange button that said “Transmit my returns now?”  If so, your return is now in “pending” on a server.  Do not try to change anything while your return is in pending. If your return is rejected you will be able to make corrections before re-filing.

The IRS will not be accepting/rejecting 2020 returns until Friday, February 12, 2021.  You need to watch your emails for the acceptance/rejection notice that may take until mid-February or later to arrive.   And watch your spam folder too.

When you e-file your federal return you will receive two emails from TurboTax.  The first one will say that your return was submitted.  The second email will tell you if your federal return was accepted or rejected.  If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.

A state return cannot be accepted until the federal return has been accepted.

https://www.irs.gov/newsroom/2021-tax-filing-season-begins-feb-12-irs-outlines-steps-to-speed-refund...

We do not know if entering the wrong stimulus amount will delay your refund --- or for how long if it does.   The IRS has not offered any guidance yet on how they will handle returns that have incorrect stimulus amounts entered.  We all just have to wait and see.

I also accidentally place a higher number than I realized when reading my bank statements. Is there any effect on my refund? I have proof that I got the correct amount but I don’t know if I should change or amend the tax file after?

I also accidentally place a higher number than I realized when reading my bank statements. Is there any effect on my refund? I have proof that I got the correct amount but I don’t know if I should change or amend the tax file after?

There is NOTHING you should or can do ... once the IRS starts processing returns then they will automatically correct any errors in that section ... they did say this could delay the return but it is unknown for how long. 

The tax return will remain as Pending until the IRS starts accepting or rejecting 2020 tax returns on February 12, 2021.

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.

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions