no, she not died. she later reappears in the manga.
But all of that vanished within a few minutes of Saitama's arrival because Mosquito Girl died instantly from one slap delivered by Saitama. Her blood could even be seen spraying everywhere when her body exploded.
On the other side of the coin, my part as an author, I'm using this period to set the base for important characters for future chapters and show what kind of relationship Itachi shares with these people, and how it all comes full circle in the story.
For the first time in a very long time, Kenpachi desired more strength. And not because he wanted to defeat someone stronger, but because he wanted to defeat someone weaker than himself.
It was a sniping duel, and Tang Yu, sitting in the passenger seat with the window down, was also at risk. They couldn't maintain a constant speed and give the enemy the perfect sniping opportunity.