I think your logic "Therefore no Gentile/Believer is obligated to any of the 10 commandments or 613 Commandments." does not bear up to the scriptures.
When the Israelites fled from Egypt after the Passover, many non-Israelites fled with them. If one is a Gentile, isn't he/she a non-Israelite?
Exo_12:49 One law shall be to him that is homeborn, and unto the stranger that sojourneth among you.
Num 15:15 One ordinance shall be both for you of the congregation, and also for the stranger that sojourneth with you, an ordinance for ever in your generations: as ye are, so shall the stranger be before the LORD.
Num_15:16 One law and one manner shall be for you, and for the stranger that sojourneth with you.
Num 15:26 And it shall be forgiven all the congregation of the children of Israel, and the stranger that sojourneth among them; seeing all the people were in ignorance.
Num_15:29 Ye shall have one law for him that sinneth through ignorance, both for him that is born among the children of Israel, and for the stranger that sojourneth among them.
Num 15:30 But the soul that doeth ought presumptuously, whether he be born in the land, or a stranger, the same reproacheth the LORD; and that soul shall be cut off from among his people.
In the end, we find that the New Jerusalem that comes down from heaven has 12 gates, each one made from a pearl. On each of the 12 gates is the 12 names of tribes of Israel. Where is the gate for the Gentiles?
Rev 21:12 And had a wall great and high, and had twelve gates, and at the gates twelve angels, and names written thereon, which are the names of the twelve tribes of the children of Israel:
Rev 21:21 And the twelve gates were twelve pearls; every several gate was of one pearl: and the street of the city was pure gold, as it were transparent glass.
Rev 21:22 And I saw no temple therein: for the Lord God Almighty and the Lamb are the temple of it.
Rev 21:23 And the city had no need of the sun, neither of the moon, to shine in it: for the glory of God did lighten it, and the Lamb is the light thereof.
Rev 21:24 And the nations of them which are saved shall walk in the light of it: and the kings of the earth do bring their glory and honour into it.
Rev 21:25 And the gates of it shall not be shut at all by day: for there shall be no night there.
Rev 21:26 And they shall bring the glory and honour of the nations into it.
Rev 21:27 And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.
Deu 29:14 Neither with you only do I make this covenant and this oath;
Deu 29:15 But with him that standeth here with us this day before the LORD our God, and also with him that is not here with us this day:
Joh 7:16 Jesus answered them, and said, My doctrine is not mine, but his that sent me.
Mal 3:6 For I am the LORD, I change not; therefore ye sons of Jacob are not consumed.
Heb 13:8 Jesus Christ the same yesterday, and to day, and for ever.
2Ti_3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
Joh 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
Joh 1:2 The same was in the beginning with God.
Joh 1:3 All things were made by him; and without him was not any thing made that was made.