Filed 21 & 22 tax returns for parent, spouse died in 20, Shouldn't her status for 21 and 22 be QSS vs. Single? TT chose single. Shouldnt it be SSQ? how to amend?

If the spouse died in 2020, the 2020 return could be filed as a joint return.  If there were no dependent children being claimed for 2021 or 2022 then the filing status is Single.   Qualified Surviving Spouse is used if the surviving spouse is still supporting qualified children.

You mean Qualifying Widow?  

You can file a Joint return the year your spouse died.  For the next two years following a husband's or wife's death, the surviving spouse can file as a qualifying widow or widower if they have a qualifying child. That basically lets you continue to use the same tax brackets that apply to married-filing-jointly returns.  After the year of death if you don't have a child you file as Single.

See the eligibility rules on page 9 of IRS publication 501

https://www.irs.gov/pub/irs-pdf/p501.pdf

See Turbo Tax help article

https://ttlc.intuit.com/community/using-turbotax/help/how-should-i-file-my-return-if-my-spouse-recently-died/01/26367