First of all, we’d like to make it clear that in Islam, contacts between men and women are permissible as long as both parties adhere to the teachings of Islam and ethical morals. There is nothing wrong that men and women co-operate together on that which is lawful and permissible such as acquiring beneficial knowledge or good work.

As regards the issue of mixing between people of the opposite sex who are not mahrams, we would like to quote for you the following by the eminent Muslim scholar Sheikh Yusuf Al-Qaradawi: “In principle, contacts between men and women are not totally rejected; rather, recommendable so long as a noble objective is intended and the subject itself is lawful such as acquiring beneficial knowledge, good work, charitable project, obligatory Jihad or many other deeds that require the efforts and the co-operation the both sexes.
However, this by no means calls for transgressing the limits and forgetting about the nature of both sexes. In all their dealings, both men and women are to abide by the teachings of Islam that call for co-operation on the basis of goodness and piety while observing the rules of morality and politeness.

The following are the conditions that must be met when there is a contact between both sexes:
1- Both parties should adhere to lowering the gaze. No lustful look should exist. Almighty Allah says: [Tell the believing men to lower their gaze and be modest. That is purer for them. Lo! Allah is aware of what they do. And tell the believing women to lower their gaze and be modest, and to display of their adornment only that which is apparent, and to draw their veils over their bosoms, and not to reveal their adornment save to their own husbands or fathers or husbands’ fathers, or their sons or their husbands’ sons, or their brothers or their brothers’ sons or sisters’ sons, or their women, or their slaves, or male attendants who lack vigour, or children who know naught of women’s nakedness. And let them not stamp their feet so as to reveal what they hide of their adornment. And turn unto Allah together, O believers, in order that ye may succeed.]  (An-Nur: 30-31)
2- A Muslim woman should observe the Muslim code of dressing. The Muslim dress for women, as well-known, covers the whole body save for the face and the hands. It is neither tight nor light in a way that describes the features of the body.
3- General morality should be adhered to. In other words, a woman should be serious in speech and decent in way of walking, nipping any trial of Satan to spread immorality in the bud. Also, no perfumes are to be worn while being away from home, for the Prophet (peace and blessings be upon him) said: “Any woman who wears perfumes and then passes by a group of men and they smell it, she is an adulteress.”
4-No man and woman are allowed to be together in a place where no other males exist, for the Prophet (peace and blessings be upon him) said: “(Doing so) their third mate will be Satan i.e. leading them to sin.” This applies also to the relatives of the husband as the Prophet (peace and blessings be upon him) said: “Beware of sitting with women alone!” They (the Companions) said: “What about the relative of the husband, O Messenger of Allah?” He said: “A relative of the husband is death i.e. the cause of death.” This is because a relative of a husband may stay for a long time and thus the danger of sin becomes greater.
5- Finally, we would like to note that all these contacts are not to be given loose rein. They are to be carried out according to need and reasonable interaction. Contacting men, no Muslim woman is allowed to forget about her nature or her role as a woman and instructor of all Muslim generations.”

Given the above, we’d like to stress that the above-mentioned guidelines apply to cousins and other relatives who are not mahrams. So, generally speaking, it is permissible for cousins to share problems and have some sort of friendship which is represented in kinship without violating the manners of Islam regarding the ethics and manners of mixing and talking between people of the opposite sex.