BTDT:"She felt no shame because her conscience was clear (already purified by God's eternal spirit) Hebrews 9:14..."
Hebrews 9:14How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death,[a] so that we may serve the living God!
Why would you use such text to explain "she felt no shame". This has to do with believers. (she was not a believer) She did feel shame, that is why she did not go to draw water from the well at the same time as all the other women because they caused her to feel convicted. Without that conviction (the law) and without the Holy Spirit, she probably would not have ever cared about her lifestyle and would not have sought out the Living Water that Jesus taught her. She would have been a happy camper in her sins if someone (people or Holy Spirit) had not stirred her to realize her faults.
Hebrews 15For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance—now that he has died as a ransom to set them free from the sins committed under the first covenant.
That is why when Jesus came on the scene and spoke to her, she was already in an awareness that she needed "something". (she didn't know what "something" was)
When is the right time to point out faults or sins to an unbeliever?" I would not think you would do it right off the bat if they are not open to your message. People will put up a wall and shut the message out but eventually the issue must be approached.
Without "the law", (first covenant) one would not feel the conviction to even need Living Water. Once you accept the new covenant of Christ, your past sins are forgotten (washed away) and you receive the Holy Spirit of Truth and Power.