Scripture clearly proves you wrong.
Acts 11:14 (KJV) "Who shall tell thee words, whereby thou and all thy house shall be saved."
Saved means saved here, not 'made whole'. Or has the KJV, and all other versions, translated the word wrongly? It plainly says Cornelius would not be saved until Peter spoke the gospel to him. Nobody in this dispensation can be saved without hearing the gospel.
Rom 1:16 "For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek."
Being acceptable to God does not mean saved. Peter is saying that Gentiles who seek God were now admissible into the Kingdom. Not that they were yet Christians. Fearing God and performing good works, without hearing about Christ, does not make someone a Christian.
No, simply doing good deeds does not make you a born again Christian. Mormons and Jehovah's witnesses do good works, are they born again? Many non-Christians do good works, are they born again? You are completely twisting 1 John 2:29. It says
"you know that everyone also who practices righteousness is born of Him." It is speaking of how to recognize born again believers. Good works are a characteristic of believers, not what makes them believers. Scripture makes it absolutely clear that good works are useless to save:
Eph 2:8-9 "For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God—not by works"
Galatians 2:16 "know that a person is not justified by the works of the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in[a] Christ and not by the works of the law, because by the works of the law no one will be justified."
Philippians 3:9 "and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ—the righteousness that comes from God on the basis of faith."
Romans 3:28 "For we maintain that a person is justified by faith apart from the works of the law."
Romans 4:5 "However, to the one who does not work but trusts God who justifies the ungodly, their faith is credited as righteousness."
Romans 11:6 "And if by grace, then it cannot be based on works; "
Isaiah 64:5-6 "How then can we be saved? All of us have become like one who is unclean, and all our righteous acts are like filthy rags;"
We can only be born again by hearing the gospel:
1 Peter 1:23-25 "Since you have been born again, not of perishable seed but of imperishable, through the living and abiding word of God.....And this word is the good news that was preached to you."
Rom 10:13-17: For “everyone who calls on the name of the Lord will be saved.” How then will they call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching?...So faith comes from hearing, and hearing through the word of Christ.
No, you are twisting scripture yet again. In Peter's vision, God does not say that Cornelius and the Gentiles have now been made clean, by which you mean clean from sin, ie saved. Here is the verse in context:
Acts 10:12-15 "In it were all kinds of animals and reptiles and birds of the air. And there came a voice to him: “Rise, Peter; kill and eat.” But Peter said, “By no means, Lord; for I have never eaten anything that is common or unclean.” And the voice came to him again a second time, “What God has made clean, do not call common.”
The cleansing was to do with the prohibited food in the vision - removing the distinction between clean and unclean animals in Jewish Law. All the food in sheet was declared ok to eat. It was symbolic of removing the distinction that existed between Jews and Gentiles. It doesn't say the Gentiles were now cleansed of sin. Nobody is cleansed from their sin until they trust in Christ and are washed in the blood of the Lamb.
1 John 1:7 "and the blood of Jesus Christ his Son cleanseth us from all sin"
1 Peter 1:18-22 "you were not redeemed with corruptible things....But with the precious blood of Christ, as of a lamb without blemish and without spot..... Seeing you have purified your souls in obeying the truth"