Acts 10:44-47
While Peter was still speaking these words, the Holy Spirit fell upon all those who heard the word.
It is clear to me that they heard the word and the H.S. fell upon them.
45 And those of the circumcision who believed were astonished, as many as came with Peter, because the gift of the Holy Spirit had been poured out on the Gentiles also.
I see that the gift of the H.S. fell upon them, which would indicate that they were in right standing to receive the H.S.46 For they heard them speak with tongues and magnify God. Then Peter answered,
47 "Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?"
NKJV
I can conclude in this passage it seems to me that they had receive the gift of the H.S. before water baptism.
Acts 11:15-18
15 And as I began to speak, the Holy Spirit fell upon them, as upon us at the beginning.
I see this as Peter speaking of how the H.S. was poured out upon the twelve who received power as well, spoke in tongues (Languages) not known before this pouring out. I believe the Apostles were saved before the out pouring of the Spirit, Jesus had breathed the H.S on them in the upper room before He ascended.
16 Then I remembered the word of the Lord, how He said, 'John indeed baptized with water, but you shall be baptized with the Holy Spirit.'
This does indicate to me that Jesus baptized this man and his family with that in which He promised.
17 If therefore God gave them the same gift as He gave us when we believed on the Lord Jesus Christ, who was I that I could withstand God?"
18 When they heard these things they became silent; and they glorified God, saying,"Then God has also granted to the Gentiles repentance to life."
NKJV
Acts 15:7-11
7 And when there had been much dispute, Peter rose up and said to them:"Men and brethren, you know that a good while ago God chose among us, that by my mouth the Gentiles should hear the word of the gospel and believe.
8 So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us,
God knew the heart of Cornelius and acknowledged them by Giving the H.S.
9 and made no distinction between us and them, purifying their hearts by faith.
I see this as the fact that they were purified by the message that Peter brought to them.
10 Now therefore, why do you test God by putting a yoke on the neck of the disciples which neither our fathers nor we were able to bear?
11 But we believe that through the grace of the Lord Jesus Christ we shall be saved in the same manner as they."
This seems to say that the Jews and the Gentiles are saved in the same manner.
Acts 2:37-39
37 Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, "Men and brethren, what shall we do?"
The were convicted of the things they just heard, they wanted to know what should they do.
38 Then Peter said to them,"Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit.
It seems as if they believed already, Peter makes no mention of telling them to believe, he tells them to repent and be baptized (Holy Spirit or Water) for the forgiveness of sins; and you shall receive the gift of the H.S.
39 For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call."
NKJV
I am having a hard time harmonizing the ideas shown in Acts 10, 11, and 15 with what I see in Acts 2, Acts 8, Acts 16 (Lydia), Acts 19, Acts 22.
Its not that I am not being honest, I have already stated that much of Cornelius's conversion is very strange in light of other passages. For me it about harmonizing the summation of scripture when it comes to salvation and the Gospel.