Is it permissible to inform one's brother of his wife's misconduct and neglect of their daughter, knowing that the brother encourages her to pray and fast?

Your brother has committed several major sins, such as fornication and abandoning prayer. He must hasten to repent and observe prayer, for many scholars consider someone who abandons prayer out of laziness to be a major disbeliever, excluded from the Muslim community. It is not permissible for your brother to marry a fornicator (female) unless she repents and her repentance becomes apparent, based on the Almighty's saying: {The fornicator does not marry except a fornicator or a polytheist; and as for the fornicator - none marries her except a fornicator or a polytheist. And that has been forbidden to the believers.} Also, it was obligatory for him to ensure her womb was clear (by observing one menstrual cycle) before the marriage contract.

A girl born out of wedlock is not attributed to him nor related to him; rather, she is attributed to her mother.

Your brother's wife has committed major sins by abandoning prayer and fasting, and by displaying herself (tabarruj) and speaking seductively. Your brother must order her to repent, become righteous, and wear the hijab. If she complies, then that is good; otherwise, he should divorce her.