What exactly happened in the Open World Blitz Championship in game Carlsen-Alireza? In the 19th round of the World Chess Blitz Championship in Moscow, Russia, Magnus Carlsen faced Alireza Firouzja with black. Alireza lost on time while he was trying to restore a piece he dropped.

It's said that he made multiple appeals to the CA IA Takis Nikolopoulos. What exactly happened and what was the final outcome of the game?
As you said, Alireza Firouzja lost on time while he was trying to restore a piece he dropped. He appealed, but the appeal was denied. 

It was denied for several reasons.

First, he appealed about Magnus uttering one frustrating word earlier in the game. That was denied because had he wanted to appeal that, he had to do it right then and there, but he did not.

He questioned whether the clock was in proper operating order, but that was also denied.

He was declared lost because, no matter how unlikely, there was a position that Magnus could mate him in.


  Paragraph 6.9 of the FIDE Laws of Chess state:
  
  The game is drawn, if the position is such that the opponent cannot
  checkmate the player’s king by any possible series of legal moves.


It is my understanding that the formal appeal was on the Magnus' utterance as Alireza Firouzja had already been shown the rule in the rule book, so I do not believe that he formally appealed that part of the ruling.