Is the Christian claim that the Prophet, peace and blessings be upon him, killed Umm Qirfa by splitting her in half, by tying her legs to two horses, correct? And is killing in this manner permissible?

One must stay away from dubious matters, especially if there isn't sufficient scholarly immunity to refute them. The story of Umm Qirfa, Fatimah bint Rabi’ah, which the disbelievers incessantly bring up, states that the Prophet, peace and blessings be upon him, did not kill her. Rather, Zayd ibn Harithah killed her. Umm Qirfa had prepared forty horsemen, from among her children and grandchildren, to fight the Prophet, peace and blessings be upon him. So, he sent Zayd to them, and he killed them and her. She had set up her shield in Medina between two spears. A female combatant is killed, and Umm Qirfa was a combatant and incited fighting. As for the narrations about her mutilation, such as tying her to horses' tails and tearing her apart, they are weak and unproven, and Islam forbade mutilation.