Is touching a girl with the hands from the outside, without penetration, considered zina (fornication/adultery)? And does the noble verse apply to it: "And give tidings to the killer of being killed, and to the fornicator of poverty, even if after a while"? And what is the punishment for this act on the Day of Judgment?

The fornication that necessitates a Hadd (prescribed punishment) is the insertion of the glans penis into the vagina. There is also fornication that is sinful but does not necessitate a Hadd, such as gazing (at forbidden things), enjoying the voice of a non-mahram woman, and touching her. This is in accordance with the saying of the Prophet, peace and blessings be upon him: "The son of Adam has his share of adultery decreed for him, and he will inevitably realize it. The adultery of the eyes is gazing, the adultery of the ears is listening, the adultery of the tongue is speaking, the adultery of the hand is touching, and the adultery of the foot is stepping. The heart yearns and wishes, and the private parts either confirm that or deny it."

As for the phrase "Give glad tidings to the murderer of being killed, and to the fornicator of poverty, even if after a while," it is not a Quranic verse but a weak hadith. The punishment of the fornicator on the Day of Judgment depends on his repentance. Whoever repents with sincere repentance, Allah will forgive him. Otherwise, he is under the will of Allah; if He wills, He will punish him, and if He wills, He will forgive him for sins lesser than Shirk (associating partners with Allah). One should avoid mixing with women and being alone with them.