is ms office 2011 compatible with latest IOs?

If you mean the latest macOS, no, it's not. You'll need to either by the current standalone version or subscribe to Office 365.

Support for Microsoft Office 2016 ended on October 13, 2020.

Currently-patched Office 2016, Office 2019, the upcoming Office 2021, and the Office 365 subscription are all 64-bit apps and reportedly all do work with Catalina 10.15 and Big Sur macOS 11.

The oldest of Office 2016 was not 64-bit, but was updated to be 64-bit with the 15.25 version, and later.

How long 2016 continues to work? Whether it works for you? When it stops working?

Alternatives to purchasing Office 2019, or the upcoming Office 2021 arrives later this year, or an Office 365 subscription, include the free LibreOffice package, and Apple iWork can read and write many Office documents in addition to the Apple iWork document formats.

To extend the correct answer above, Microsoft Office 2011 won’t work in macOS Catalina and later.

Office 2011 and earlier are 32-bit apps, and no 32-bit apps will work on macOD Catalina or the current macOS Big Sur.

Alternatives to purchasing Office 2019, or the upcoming Office 2021 later this year, or an Office 365 subscription, include the free LibreOffice package, and Apple iWork can read and write many Office documents in addition to the Apple iWork document formats.

LibreOffice and the Apple iWork apps Numbers, Pages, and Keynote are free.

Is ms office 2016 compatible with Big Sur?

Is ms office compatible with the latest Big Sur?