@Yurichan300 Hata no Kokoro is from Touhou 13.5: Hopeless Masquerade, and is the main antagonist from that game.

In general, if you're looking for more information about the many, many, many characters in the Touhou universe, the Touhou Wiki is a really good resource. It's definitely nice to know about the more obscure characters, as they also have pretty interesting backgrounds and personalities.

Who is the doll being clubbed by doll Eirin?

That would be Junko from Touhou 15: Legacy of Lunatic Kingdom.

In the plot line she's responsible for leading an invasion against the Lunarians and the Lunar Capital. Hence probably why doll Eirin is beating doll Junko.