1.is it a sin to make fun of people who commit sins,or take them as a joke and laugh at them? 2.if you grow old does the relationship stay the same with non-mahram,such as you can't make friends with them? 3.can kids under the age of puberty be friends with the opposite gender?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Mocking people or ridiculing them is forbidden; Allaah Says (what means): {O you who have believed, let not a people ridicule [another] people; perhaps they may be better than them; nor let women ridicule [other] women; perhaps they may be better than them. And do not insult one another and do not call each other by [offensive] nicknames. Wretched is the name [i.e. mention] of disobedience after [one’s] faith. And whoever does not repent — then it is those who are the wrongdoers.}[Quran 49:11]

Therefore, it is not permissible for a Muslim to mock another Muslim even if the latter is sinful, as there is another prohibition in doing so because by doing so one aids the devil over him. Abu Hurayrah narrated: “A man who drank wine was brought to the Prophet and the Prophet said: “Beat him.” Abu Hurayrah said: “Some of us beat him with their hands, some of us with their shoes, and some others with their clothes (by twisting it like a lash). When the man went away, some of us said to him: “May Allaah disgrace you.” Thereupon, the Prophet said: “Do not say this, do not aid the devil over him.” [Al-Bukhari]

Hence, a righteous Muslim should know the bounties of Allaah on him by being steadfast on the religion of Allaah, so he should wish the same for others who were deprived of it. A person should observe this deprived person with merciful eye and be kind to him. Ibn Katheer said in his Tafseer quoting Al-Hassan Al-Basri: “A believer is always a sincere adviser and not a cheater.” This is in regard to the first part of your question.

Another issue should be mentioned, which is about backbiting a dissolute person, we have already issued Fataawa 81748 and 89115 clarifying its permissibility with some conditions, among which is that there is a benefit of warning people against him and the like, and not in order to avenge him and so forth.

As regards the second part of your question, it is neither permissible for a woman to establish an affectionate relationship with a non-Mahram man, nor is it permissible for a man to establish an affectionate relationship with a non-Mahram woman, as temptation can happen even in old age, as an Arabian proverb says: “Any despised matter in the sight of one person, could be a matter of importance to another.” So, a woman may attract some men even though she is elderly.

In regard to a boy who is below the age of puberty, even if he is not Mukallaf (competent for religious assignments), then if he is adolescent, he should be prevented from making friends with girls; Allaah Says (what means): {…and not expose their adornment [i.e. beauty] except to their husbands, their fathers, their husbands fathers, their sons, their husbands’ sons, their brothers, their brothers’ sons, their sisters’ sons, their women, that which their right hands possess [i.e. slaves], or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women.}[Quran 24:31]

Ibn Katheer said: “Because they are so young they do not understand anything about women or their `Awrah or their soft speech or their enticing ways of walking and moving. If a child is small and does not understand that, then there is nothing wrong with him entering upon women, but if he is an adolescent or approaching adolescence, and he knows and understands these things, and can make a distinction between who is beautiful and who is not, then he should not be allowed to enter upon women.”

Allaah Knows best.