We are US Citizens and were outside the US (all family) for more than six months. Do I qualify for EIC as my trip was due to a family emergency and I kept a permanent US address (not residence) during my time outside USA. We received a form from IRS to claim EIC, but I am not sure if I need to include a cover sheet with the form explaining the whole situation?
No, you cannot claim the Earned Income Tax Credit if you were not living in the United States for more than six months. See Residency Test.
There was a limited exception to this rule for 2020 and 2021 for Covid related absences, but it no longer applies.
The form I received from IRS was for my 2021 returns and I had difficulty in getting back to the US due to covid related travel restrictions in 2021. This is the last year I can submit the form I received from IRS to claim my EIC from 2021?
No. As MaryK4 mentioned, there was a limited exception to this rule for 2020 and 2021 for Covid related absences, but it no longer applies.
Don't I have 3 years to claim it since it was for my 2021 returns?
Yes. You have 3 years to file a return, so you have until April 18th 2025 to file a 2021 return to claim a refund.
However, the rules for 2021 do state that you must have lived in the US for more than half of the year in order to claim the EITC. 2021 Pub 596
A US address is not the same as a permanent US residence.