I have a couple of questions for you, and if you can answer them correctly, then you should have the answers to some of your own questions as well.
Before I ask you my two questions, let's quickly establish a couple of facts:
1. Cornelius was a Roman centurion.
"There was a certain man in Caesarea called Cornelius, a centurion of the band called the Italian band," (Acts 10:1)
2. Peter said that it was "unlawful" for a Jew to keep company or come unto one of another nation.
"And he said unto them, Ye know how that it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath shewed me that I should not call any man common or unclean." (Acts 10:28)
Now, here are my two questions:
1. If it truly was "unlawful" for a Jew to keep company or come unto one of another nation, and, in this particular case, the home of a Roman centurion, then why was Jesus, the consummate Jew, willing to do so himself?
Matthew chapter 8
[5] And when Jesus was entered into Capernaum, there came unto him a centurion, beseeching him,
[6] And saying, Lord, my servant lieth at home sick of the palsy, grievously tormented.
[7] And Jesus saith unto him, I will come and heal him.
[8] The centurion answered and said, Lord, I am not worthy that thou shouldest come under my roof: but speak the word only, and my servant shall be healed.
[9] For I am a man under authority, having soldiers under me: and I say to this man, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it.
[10] When Jesus heard it, he marvelled, and said to them that followed, Verily I say unto you, I have not found so great faith, no, not in Israel.
[11] And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven.
[12] But the children of the kingdom shall be cast out into outer darkness: there shall be weeping and gnashing of teeth.
[13] And Jesus said unto the centurion, Go thy way; and as thou hast believed, so be it done unto thee. And his servant was healed in the selfsame hour.
In other words, if Jesus, the consummate Jew, was perfectly willing to enter into the HOME of a Roman centurion, then why did Peter say that it was "unlawful"?
Was Jesus about to do something "unlawful", thereby making himself unworthy of being a sinless sacrifice?
2. If entering into the home of a Roman centurion truly was "unlawful", as Peter claimed, then why did God have to show him THREE TIMES that it wasn't?
I await your reply.
In the meantime, recognize that this is yet another example of Jesus ministering to a GENTILE during his earthly ministry.
Not only that, but also recognize that this GENTILE had such a "GREAT FAITH" that Jesus hadn't even found anywhere "IN ISRAEL" (Matt. 8:10).