How should we respond to faults we see in others? It's in the Bible, Matthew 7:1-2, NIV. "Do not judge, or you too will be judged. For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you."
We should respond to others' faults with mercy and patience. It's in the Bible, Ephesians 4:2, TLB. "Be humble and gentle. Be patient with each other, making allowance for each other's faults because of your love."
Is it ever right to tell a brother of his faults? It's in the Bible, Matthew 18:15, NIV. "If your brother sins against you, go and show him his fault, just between the two of you. If he listens to you, you have won your brother over."
In what spirit should this work of pointing out faults be done? It's in the Bible, Galatians 6:1-3, TLB. "Dear brothers, if a Christian is overcome by some sin, you who are godly should gently and humbly help him back onto the right path, remembering that next time it might be one of you who is in the wrong. Share each other's troubles and problems, and so obey our Lord's command. If anyone thinks he is too great to stoop to this, he is fooling himself. He is really a nobody."
"We should respond to others' faults with mercy and patience."
And if they do not listen to you you can treat them like a Pagan right.
Matt.18:15-17 is your reference, I assume?
So, how are we supposed to treat a pagan? Do we revile them? But that will not win them to the truth. So surely the next thing to do would be to take them to the basics of scripture. The fundamental of the scripture is to bring someone into a saving relationship with Jesus Christ - to make a disciple.
The greatest privilege that we have on this earth is to be used of God to lead someone to Christ. That does not mean that we excuse or ignore sin but it does mean that the goal is not to point out someone's sin - that is not the end game. I accept that there may be a need to clearly point out and expose false doctrine but we must all remember that Christ does not want anyone to be lost. We are all sinners in need of a saviour.
Treat them like a pagan? Yes, if that means leading them into the truth - and that is what it means. We should not be like some who will consign anyone who does not agree with them to hell. All that shows is a weakness, or lack, in our own understanding.
We have a precious legacy of rightly dividing the Word of God but at the same time we should remember to always reflect Christ, a loving Saviour who desires the best for us and has made provision for all to be saved if they will surrender to Him.