Is the understanding that necessitates prohibiting kissing mahrams, such as one's paternal aunt, maternal aunt, and sister, on the cheek, based on the hadith: "For one of you to be stabbed in his head with an iron needle is better for him than to touch a woman who is not lawful for him," and given that there is no proof of the permissibility of kissing them, correct? And is there any proof of the permissibility of kissing mahrams (other than one's daughter) on the cheek?

Kissing a mahram (a close relative one cannot marry) is permissible under the conditions that there is no lust and no fear of fitna (temptation or discord). The idea that the hadith "For one of you to be stabbed in the head with an iron needle is better than for him to touch a woman who is not permissible for him" includes one's daughter is an incorrect understanding; rather, it refers to a non-mahram woman. The evidence for the permissibility of kissing mahrams other than one's daughter includes the mentioned proofs: the Prophet (peace and blessings be upon him) and Abu Bakr kissing their daughters, Khalid ibn al-Walid kissing his sister, and by analogy with the permissibility of shaking hands with mahrams. This is provided that the kissing is on the forehead or head, not the mouth.