10:28 He said to them, "You yourselves know how it is an unlawful thing
for a man who is a Jew to join himself or come to one of another nation,
but God has shown me that I shouldn't call any man unholy or unclean. 
10:29 Therefore also I came without complaint when I was sent for.
I ask therefore, why did you send for me?" 

10:30 Cornelius said, "Four days ago, I was fasting until this hour, and at the ninth hour,{3:00 P. M.}
I prayed in my house, and behold, a man stood before me in bright clothing, 
10:31 and said, 'Cornelius, your prayer is heard, 
and your gifts to the needy are remembered in the sight of God. 
10:32 Send therefore to Joppa, and summon Simon, who is surnamed Peter. 
He lodges in the house of Simon a tanner, by the seaside. When he comes, he will speak to you.' 
10:33 Therefore I sent to you at once, and it was good of you to come. 
Now therefore we are all here present in the sight of God 
to hear all things that have been commanded you by God." 

10:34 Peter opened his mouth and said, "Truly I perceive that God doesn't show favoritism; 
10:35 but in every nation he who fears him and works righteousness is acceptable to him. 
10:36 The word which he sent to the children of Israel, 
preaching good news of peace by Jesus Christ--he is Lord of all--
10:37 that spoken word you yourselves know, which was proclaimed throughout all Judea, 
beginning from Galilee, after the baptism which John preached; 
10:38 even Jesus of Nazareth, how God anointed him with the Holy Spirit and with power,
who went about doing good and healing all who were oppressed by the devil, for God was with him. 
10:39 We are witnesses of everything he did both in the country of the Jews, and in Jerusalem; 
whom they also{TR omits "also"} killed, hanging him on a tree. 
10:40 God raised him up the third day, and gave him to be revealed, 
10:41 not to all the people, but to witnesses who were chosen before by God,
to us, who ate and drank with him after he rose from the dead. 
10:42 He charged us to preach to the people and 
to testify that this is he who is appointed by God as the Judge of the living and the dead.
10:43 All the prophets testify about him,
that through his name everyone who believes in him will receive remission of sins." 

10:44 While Peter was still speaking these words,
the Holy Spirit fell on all those who heard the word. 
10:45 They of the circumcision who believed were amazed, as many as came with Peter,
because the gift of the Holy Spirit was also poured out on the Gentiles. 
10:46 For they heard them speaking in other languages and magnifying God. 

Then Peter answered, 
10:47 "Can any man forbid the water,
that these who have received the Holy Spirit as well as we should not be baptized?" 
10:48 He commanded them to be baptized in the name of Jesus Christ. 
Then they asked him to stay some days. 
 

vs 28 reveals the purpose of the vision given to Peter earlier in the chapter. Apparently it was a revelation to Peter that he shouldn't call any may common or unclean. Before that point held such Gentiles in contempt. It appears he hadn't previously taken to heart Jesus' teachings about Gentiles. This explains why previously he wasn't obeying the great commission to make disciples of the Gentiles, but simply stayed around the Jews, while others would better understood the mystery of the faith (Ephesians 3:6) went beyond Jerusalem.

vs 34 "God is no respecter of persons:"
God's favoritism is not shown based on race. But he does favor some based on their attitude and behavior, according to the next verse.

vs 35 But in every nation he that feareth him, and worketh righteousness, is accepted with him."
Notice it doesn't say "in every religion". Jesus said, "You Samaritans worship what you do not know; we worship what we do know, for salvation is from the Jews." John 4:22 Judaism is the only true religion. And the true Judaism today is Christianity from which the unbelieving Jews have cut themselves off. Muslims fear their God. But their God is a distortion of the God of the Bible. They are anti-Christians and do not accept Jesus as the Son of God and LORD of all, as Peter calls him in verse 36. The "him" that Peter is referring to that "he that feareth" is the God of the Bible and not some other god.

Fearing God and doing works of righteousness go hand in hand. A man's fear of God is revealed by his works. In the case of Cornelius, he prayed, he gave alms and he was a just man of good report among all the Jews. (Acts 10:4,22) 

What Peter means by  "accepted with him" is that such people are appropriate candidates to invite into the kingdom by telling them the gospel. That his how he was applying it. Before his vision he reckoned even God fearing Gentiles unworthy of the kingdom just because they're Gentiles. Now the God fearing among both Jews and Gentiles are worthy to hear the gospel, and in responding they will be given the Holy Spirit as a guarantee of their inheritance. (Ephesians 1:13,14)  However I sense that even in this Peter is being too narrow. For wasn't it rather the sinners, tax collectors and prostitutes who were more characteristic of those who responded to Jesus, and not so much those who were reckoned "good decent people" in the society? Formerly Peter classified people by race, and now by their fear of God and their righteous works. But if you view the Bible as a whole it seems to me that God favors neither based upon race nor upon works, but upon their level of humility. Was this not Jesus' teaching in the parable of the Pharisee and the Tax Collector? And didn't God say, "I live in a high and holy place, but also with him who is contrite and lowly in spirit, to revive the spirit of the lowly and to revive the heart of the contrite." Isaiah 57:15 and also "This is the one I esteem: he who is humble and contrite in spirit, and trembles at my word."Isaiah 66:2 He got the fear of God right. But Peter had more lessons to learn.

vs 36 "He is LORD of all." Peter wanted him to understand that Jesus was not simply the messenger, but the message as well. Accepting Jesus as LORD is essential to qualify for salvation, as Paul writes: "That if you confess with your mouth, "Jesus is Lord," and believe in your heart that God raised him from the dead, you will be saved." Rom 10:9 The Lordship of Christ must a part of the gospel message and not simply some "by the way" addition at some later date.

vs 37 "Ye know" is actually in the perfect tense "You have known", which makes sense. Cornelius had known about Jesus to an extent. Peter may have learned this fact from his servants who he spent the last few days with. But this was not unusually as Jesus had been a very public figure.

vs 38-41 Peter is not being comprehensive because Cornelius already knew alot of this. He was just summarizing. The miracles that Jesus did are an essential part of the message to affirm his claims. He also mentioned his death and resurrection. The resurrection should always be mentioned when the gospel is preached.

vs 42-43 It is Jesus Christ and not God the Father who people will have to face in judgement. The Father has given this responsibility to the Son. For the Christian Jesus is both judge and defense attorney. "The living and the dead" I think refers not to different judgements but simply another way of saying "everyone" regardless of they are living now, or whether they have died.

But the key verse to the gospel message is verse 43. Cornelius may have already heard much of rest of the message. But it was upon Peter revealing this final key which opened the door for the Holy Spirit to come, Cornelius and his household of course having also come to believe it. This final step to be saved is to believe his promise that your sins have been forgiven though faith in him. This is the way that God imputes righteousness throughout the Bible - through faith in the promise of God. Abraham, a Gentile at the time, was reckoned righteous by faith.  Ge 15:6  "Abram believed the LORD, and he credited it to him as righteousness." And so now it is by faith as well, that God may graciously offer this gift of the forgiveness of sins to all - both Jews and Gentiles.

vs 44-46  Their speaking in tongues was an indication that they had received the Holy Spirit. That's what happened in this case. But that is not to say that such is what happens in every case when one receives the Spirit. Putting one's faith in experiences like tongues is not putting one's faith in the atoning work of Christ. And the object of faith is the Lord Jesus Christ, and not the Holy Spirit.

The other Jews, being racist, were amazed that these Gentiles whom they looked down upon recieved the Holy Spirit. To a degree it was humiliating experience for them, as now they had to accept the fact that they were going to have to call Gentile believers "brothers". How disgusting! For a while there would be a conflict in the church over this issue as the Jewish Christians overcame their xenophobia.

vs 47-48 When did Cornelius and his house receive the Spirit? Was it before they were water baptized or after? Not after but before! There are those who, in the Spirit of the group of the circumcision, say that you have to get wet to get saved. There are those, for example, in the Church of Christ who hold that conviction. If they had been there, they also would have been astonished, but not at the fact that Gentiles recieved the Spirit. Rather they would have been astonished that they received the Spirit before getting water baptized. It is of couse appropriate to get baptized, having put one's faith in Christ. But in both these cases of the group of the circumcision and the group of the Baptism,  people put symbolism over substance and obsess over the flesh while neglecting the spirit. They throw out the baby and keep the bath water.