What are the authentic hadiths regarding looking at and touching non-mahram women, and are "For me to be thrown headfirst from the sky to the earth is better than for me to see the thigh of a woman" and "For me to be struck on the head with an iron awl is better than for me to touch the shoulder of a woman" authentic hadiths?

The hadith: "For one of you to be stabbed in the head with an iron needle is better for him than to touch a woman he is not lawful to marry" is authentic, narrated by Al-Tabarani and Al-Bayhaqi, and authenticated by Al-Albani. As for the hadith: "For me to fall from the sky to the earth is better for me than to see the thigh of a woman," we are not aware of it being a hadith.