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The case of Cornelius is very puzzling to me in many ways, and I do not have his conversion totally figured out. All I know is that the people called Christians in the New Testament were repentant, believing, immersed individuals.
You see? You are trying to figure out how to make these examples like Cornelius fit your supposed new found "enlightenment". That is not the way to study the scriptures and form sound doctrines. You are doing the exact opposite of what you set out to do. You are not letting the full counsel of God's word form the doctrine.
I pray God you will see that something has triggered an apostasy within you. You have even rejected God's family which He Himself has established in many "denominations" throughout this world for our well being, to guard us against the very thing that has happened to you. You have isolated yourself, you have strayed from the flock and from the safety and benefits found in God's people.
You won't spiritually thrive alone brother, you will slowly wither and fall prey to more and more confused thoughts. And you will bring your family down with you of whom you are responsible for before God.
I pray you will reconsider your decision to leave God's institution.
Eph 4:11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;
Eph 4:12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ:
Eph 4:13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ:
Eph 4:14 That we [henceforth] be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, [and] cunning craftiness, whereby they lie in wait to deceive;
1Cr 12:21 And the eye cannot say unto the hand, I have no need of thee: nor again the head to the feet, I have no need of you.
Can you alone be all the parts necessary for your family's spiritual well being? Absolutely not. To say you can be is to denouce God's word that says you cannot be. WE are called to be part of a local assembly for our edifying.
You are in a dangerous place brother. I pray God you will follow His plan.