If I fully withdraw my 401k, I will receive $9,000 after the 20% tax fee. How much should I expect to pay in fee/taxes next year (2021)? I'm in the 12% tax bracket.

Are you gong to be older than 59 1/2 when you do this?  If not, you will also be subject to a 10% early withdrawal penalty plus ordinary income tax.  The custodian of the account will withhold tax  just like you have tax withheld from your paychecks,  When all of your income is entered into your tax return TT will calculate your tax due or refund.

The 20% is not a tax fee; it is withholding.  If 20% is withheld, that can be enough to cover the ordinary income tax you will owe on the withdrawal.  However, it is usually not enough to cover the tax and penalty.  If you are under 59.5 years old when you take the distribution, you will owe an additional 10% penalty.  

You say you are in a 12% tax bracket, but keep in mind that the additional income (the before tax gross amount) may bump you up to a higher tax bracket.