Is it permissible for an employee whose salary is insufficient to meet his and his children's needs to take money or accept financial support for his needs from a friend who gives him charity from his private funds?

If your salary is insufficient to cover your basic needs and the needs of those you support, there is no sin upon you in taking zakat to complete what is sufficient for you. As for voluntary charity (sadaqat al-tatawwu'), it is broader than obligatory zakat, and it is permissible to give it to the rich and to those who are not poor, although it is better to give it to the needy.