Here is the key clarification. "Assurance is of the essence of believing in Jesus for everlasting life. That is, as long as a person believes in Jesus for everlasting life, he knows he has everlasting life (John 5:24; 6:35, 47; 11:27; 1 John 5:9-13)."
In other words until a person believes that what he has received from the Lord Jesus is permanent and cannot be lost, whether he understands that as eternal life, salvation or living forever with Him in His kingdom, he is not yet born again. A person cannot believe in Christ alone for his eternal destiny and also believe that he can do something to keep it since he didn't earn it in the first place.
Let's say you are witnessing to someone and he indicates that he has come to faith in Christ as a result of what you said. To make sure he really got it, you ask him a diagnostic question: "What if you leave here and you fail to live your life for Christ; you don't join and attend a church; you don't read the bible; and instead you become an alcoholic and a womanizer and then next year you commit suicide? What would your eternal destiny be then?" If the person sad, "Oh well, then I'd go to hell," you would know that the person didn't understand. By his death on the cross the Lord Jesus took away the sins of the world (John 1:29; 1 John 2:2).
Sin is no longer an issue. Works is no longer the issue. Life and death is the issue. Once a person believes in Jesus for eternal life (John 3:16; 1Tim 1:16), they know they have eternal life.
They know falsely. It depends what one does with his belief (Matthew 25, Apoc. 22:12, Romans 2:6-9, 1 Cor. 3:9-17, James 2:17-26, 2 Peter 1:2-1).
Huh? Sin is very much an issue. Heb. 9:12 tells us that Christ's sacrifice secured our redemption, but redemption is not the same thing as salvation. We participate in and hope for salvation. Our hope in salvation is a guarantee if we are faithful to Christ to the end. But if we lose hope and fail to persevere, we can lose our salvation. Thus, by our own choosing (not by God's doing), salvation is not a certainty.