I don't see how your verses show Cornelius wasn't a proselyte.
Second, many, many non-Jews had already been justified by faith before Cornelius.
Daniel 4:34-35,37
“After this time had passed, I, Nebuchadnezzar, looked up to heaven. My sanity returned, and I praised and worshiped the Most High and honored the one who lives forever. His rule is everlasting, and his kingdom is eternal. All the people of the earth are nothing compared to him. He does as he pleases among the angels of heaven and among the people of the earth. No one can stop him or say to him, ‘What do you mean by doing these things?’
“Now I, Nebuchadnezzar, praise and glorify and honor the King of heaven. All his acts are just and true, and he is able to humble the proud.”
The Spirit was given to Cornelius and his household as a sign to Peter that the New Covenant was given to all nations, tribes, and tongues.
It was not my intent to show Cornelius was not a proselyte. It was my intent to show that it does not matter whether he was a proselyte or not in the matter of salvation. Fifteen hundred previous years of Law keeping proved that the law could not save anybody and only a small remnant of natural born law keeping Jews were finally saved. I will observe that it would have been very difficult for a Roman soldier to keep the Law of Moses, which included temple worship, keeping the feast days of Israel along with the Festivals and the sabbaths.and here this man is presented to us in good standing with the Roman government. Common sense says there had to be some conflicts between God's law and Caesar's law somewhere along the way.
No, the Law of Moses served it's purpose, which is stated here;
Ga 3:21 Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law.
22 But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe.
23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed.
24 Wherefore the law was our schoolmaster [to bring us] unto Christ, that we might be justified by faith.
25 But after that faith is come, we are no longer under a schoolmaster.
26 For ye are all the children of God by faith in Christ Jesus.
Now, the promise by faith of Jesus Christ of verse 22 above is clearly identified as the Spirit in this chapter. I am going to quote the identification in a single verse.
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
Galatians chapter three and the verses I have been quoting to you are a contrast between the Abrahamic Covenant and the Mosaic Covenant. The covenant with Abraham is promises of God without Abraham doing anything to secure the promises but believe them. The Abrahamic Covenant was eternal and depended upon the faithfulness of God to him while the Mosaic Covenant was a temporary codicil to the covenant and depended upon their faithfulness as the people of God and a nation to God. God did not fail but Israel did. The proof that God did not fail is that he sent his Spirit through Christ to bless Abraham and his natural seed first and by extension the nations of the world in spite of their failure.
Here is the blessing of Verse 14 above from the Abrahamic Covenant.
1 Now the LORD had said unto Abram, Get thee out of thy country, and from thy kindred, and from thy father’s house, unto a land that I will shew thee:
2 And I will make of thee a great nation, and I will bless thee, and make thy name great; and thou shalt be a blessing:
3 And I will bless them that bless thee, and curse him that curseth thee: and in thee shall all families of the earth be blessed.
Here is the contrast between the Abrahamic and the Mosaic covenants in Ga 3.
15 Brethren, I speak after the manner of men; Though [it be] but a man’s covenant, yet [if it be] confirmed, no man disannulleth, or addeth thereto.
16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ.
17 And this I say, [that] the covenant, that was confirmed before of God in Christ, the law, (t
he Mosaic Covenant) which was four hundred and thirty years after (
the Abrahamic Covenant), cannot disannul (
the promises of the Abrahamic Covenant), that it (
Mosaic Covenant) should make the promise of none effect.
18 For if the inheritance [be] of the law, [it is] no more of promise: but God gave [it] to Abraham by promise.
19 Wherefore then [serveth] the law? It was added because of transgressions, till the seed should come to whom the promise was made; [and it was] ordained by angels in the hand of a mediator.
Paul argues that the blessings of the Abrahamic covenant on Israel and the nations through Jesus Christ proves the faithfulness of God. Two legitimate principles of God's divine dealing are contrasted here. When Jesus came it ended the operative principle of God's dealing with Israel, the law, and opened up his opportunity to deal with both Israel and the nations under the divine principle of faith. Not just faith as a principle but specifically faith in Jesus Christ as the condition for the Abrahamic Covenant blessing.
22 But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ (
which is his Spirit) might be given to them that believe.
23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed.
24 Wherefore the law was our schoolmaster [to bring us] unto Christ, that we might be justified by faith.
25 But after that faith is come, we are no longer under a schoolmaster.
26 For ye are all the children of God by faith in Christ Jesus.
27 For as many of you as have been baptized into Christ have put on Christ.
28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
29 And if ye [be] Christ’s, then are ye Abraham’s seed, and heirs according to the promise.
There is NO conflict in Ga 3 and the events of Acts 10 but there is explanation. The faithful God has included the nations in his blessing beginning at Cornelius the Roman.
With due respect to you AustinC, you must adjust your thinking if you will understand these great truths of God.