Enforcing the two-move rule?
Then no, not a legal move by the rebukes set chess.com uses.
Although I know some local areas, especially in Asia, have a rule like that. But not FIDE rules, and I think Chess.com follows those rules.

Correct, under the official rules of chess, the only time two pieces can be moved at once is during castling.
Please, do not question uncle Jalavan's authority. He is a local master who beats computer's highest level.
Yes, we call it "uncle Jalavan's caravan", because the two pawns resembles a caravan of camels in the desert. Others play this as well: https://www.chess.com/forum/view/general/moving-two-pawns-in-the-opening

Please, do not question uncle Jalavan's authority. He is a local master who beats computer's highest level.
What is the computer's highest level; a 1200 or a 3300+ Komodo engine?
Please, do not question uncle Jalavan's authority. He is a local master who beats computer's highest level.
What is the computer's highest level; a 1200 or a 3300+ Komodo engine?
Uncle Jalavan says 5000 rating strength.

How can I perform the two-move rule in the opening? I.e. moving two pawns one square each instead of moving one pawn two squares.
This is necessary for performing the Jalavan-gambit, named after my uncle Jalavan, who taught me everything about chess.
The version of chess played on chess.com is a simplified version geared toward the masses. Your uncle was teaching you the more complicated version, which is too difficult for most people to understand. If chess.com hosted that version, membership would drop by at least 90% - as you can see from the comments above by ignorant posters who have no idea that the version of chess they're used to playing isn't the only one that exists.
Proof of 5000 strength. This is old version. We also have new version, but it is without number. Probably higher than 5000 since it is newer.
How can I perform the two-move rule in the opening? I.e. moving two pawns one square each instead of moving one pawn two squares.
This is necessary for performing the Jalavan-gambit, named after my uncle Jalavan, who taught me everything about chess.