What happens with our I-829 petition if the main applicant have been outside of the U.S. for a long time because of Covid-19?

Unless divorced or possibly legally separated, your case is a derivative one; the dependents are dependent on the principal. He needs to return as soon as possible.

COVID-19 has caused many issues around the world and for many permanent residents being "stuck" outside of the United States due to travel restrictions, lack of available flights, or health concerns, is a huge problem, especially if their travel document has expired or if they have been absent from the United States for more than one year. If your father has a valid I-829 extension receipt or a valid I-551 passport stamp, he should attempt to return to the United States before it expires. If it has expired already, and he has been absent for more than six months but less than one year, he should apply for a transportation letter (Form I-131A) from the U.S. embassy or consulate in your home country. If he has been absent for more than one year, he probably should apply for an SB-1 returning resident immigrant visa. The way to preserve U.S. lawful permanent residence (green card status) is to maintain the intention to permanently reside in the United States. If you can show that the pandemic, not his intention to abandon his green card, is the cause of his absence, which it appears to be, then the I-829 is unlikely to be rejected for that reason.

As long as the main applicant is gone less than a year, you should be OK to retain the two-year green card (conditional permanent residency status) and continue with the 10-year green card. If the main applicant needs to be gone longer, have him return before 1 year and then apply for a Reentry Permit on U.S. soil and be fingerprinted and then he can leave and remain up to 2 years outside the U.S. provided ties to U.S. continue.

Two things: (1) look into filing separately, and (2) depending on the circumstances, your dad may qualify for a SB-1 returning-resident visa.

He should be allowed back into the country, but if he indeed abandons his residence and chooses not to return, then the dependents will not be able to be approved.