If you change bank accounts the deposit for the unemployment refund will be rejected by the bank and will go back to the IRS.   Then the IRS will have to issue and mail a check to the address on your bank account.  So you may want to keep that bank account open until you do receive the unemployment refund.

As for the child tax credit monthly payments the IRS is going to set up a portal where you can enter different banking information---but it is not ready yet.

That CTC increase is not for 2020;  it is for 2021.   Your 2020 return does not have to be amended for it.  More information will be available soon; the details of how it will be implemented have not yet been clarified fully.  There will be monthly payments going out beginning in July 2021, with some of the CTC still left as a refundable credit on your 2021 tax return next year.

https://ttlc.intuit.com/community/tax-topics/help/how-will-the-stimulus-package-impact-me/01/1393859...

https://www.irs.gov/credits-deductions/advance-child-tax-credit-payments-in-2021

https://www.irs.gov/newsroom/irs-unveils-online-tool-to-help-low-income-families-register-for-monthl...

IRS.gov/childtaxcredit2021, 

https://www.kiplinger.com/taxes/602921/child-tax-credit-update-irs-sending-letters-to-families-who-m...

https://www.kiplinger.com/taxes/602431/child-tax-credit-2021-who-gets-3600-will-i-get-monthly-paymen...

if you already filed with direct deposit info, it can not be changed. if the /c is closed you will eventually get a paper check in the mail. if you move notify the USPS and file form 8822, change of address form, with the IRS

https://www.irs.gov/pub/irs-pdf/f8822.pdf 

the new CTC does not start until 2021. advance payments will start in June or July of this year.  at some point, the IRS says it will have a portal to update information

https://www.irs.gov/credits-deductions/advance-child-tax-credit-payments-in-2021