Is it permissible to give zakat to a brother who is employed but has a low income and is in debt, and has children attending school, knowing that he does not maintain his prayers and drinks alcohol, out of fear for his children's well-being and his own imprisonment?

A person's profligacy does not prevent him from being given zakat. If giving it softens his heart, then there is no reprehensibility in it. One should strive to advise the brother and call him to repentance, and make the payment of zakat a means to soften his heart and advise him gently.