What is the ruling on dealing with a brother who exhibits signs of hypocrisy, disbelief, and atheism, such as lying, betrayal, mocking religion, not praying, and committing major sins? And is it obligatory to confront him or to remain silent about his actions?

Your brother is in great danger due to his abandonment of prayer, consumption of alcohol, and commission of immoral acts. However, he has not apostatized with certainty and should be treated as a disobedient Muslim. You must call him to Allah, explain the danger of his current state, and urge him to repent. If he responds, then all praise be to Allah. If he does not respond, then you may abandon him if abandonment is a means to reform him.