Is there any sin upon one who guides and admonishes youth if one of them disbelieves and insults the Prophet (peace and blessings be upon him), after he has tried to deter him and remind him of Allah's warning without success, and then ends the conversation with him?

Thank you for your eagerness to call people to Allah. However, you must be cautious of the dangers of conversing with men online and adhere to the conditions of dialogue outlined in Fatwa No. 30893. It is better that your da'wah be limited to women. The blasphemy and obscenities uttered by the person are his burden, and you bear no responsibility for any of it. Know that callers to Islam encounter such individuals, so you must be patient and seek reward from Allah, as He the Almighty said: (Enjoin what is right and forbid what is wrong, and be patient over what befalls you. Indeed, that is of the matters [requiring] determination).