You make a good point: We're going to have to examine scriptures which might seem to disagree with our positions, and let God correct us where we need it.
I'm surprised when people turn to scriptures about faith or repentance, or confession of Christ when the question is about baptism. If we want to learn about baptism and its place in redemption, we need to look at what the Bible says about baptism. I'm pretty sure you'd agree with that.
The case you brought up - Cornelius and his household - is a good one to look at. It is a peculiar one, being the first case of the gospel being preached to Gentiles.
Peter, being a Jew, would have been reluctant to preach to those folks, and had to be told by God to do so - hence the vision, etc. But he obeyed the Spirit's instructions, and went and preached to Cornelius. But even after preaching to them, he needed further instruction. So God poured out the Holy Spirit on these Gentiles.
It's important to note that what happened here was different from the usual receiving of the Holy Spirit. In fact, the only similar case Peter can think of is way back at Pentecost. (Recall Acts 8, where people were baptized into Jesus, and only later, when Peter and John come up and lay their hands on them, do they receive the Holy Spirit.)
As we've noted, Acts 10 is a notable case, and God gives them the Holy Spirit in a notable way. Why was this necessary? And what is the significance of it?
We find the answer in the reaction of Peter and those with him, in the reaction of the Jews in Jerusalem when Peter relates the story, and in the use Peter makes of it in Acts 15 when arguing against those who wanted the Gentile Christians to be circumcised and keep the Law of Moses: It was God's demonstration that Gentiles were eligible for salvation just as Jews were.
So Peter then asks the rhetorical question: "Can any man forbid the water, that these should not be baptized, who have received the Holy Spirit as well as we?"
Why would anyone have objected to their baptism before this? Because they were Gentiles, right? In pouring out the Holy Spirit "even as on us at the beginning" (Acts 11:15), God overruled that objection and showed that His offer of salvation was for Gentiles as well. Hence Peter's question, "who was I, that I could withstand God?"
What is he saying? What could Peter have done, at this point, that would've been withstanding God?
He didn't do it though. Instead, "he commanded them to be baptized in the name of Jesus Christ."
It's important to note that what happened here was different from the usual receiving of the Holy Spirit. In fact, the only similar case Peter can think of is way back at Pentecost. (Recall Acts 8, where people were baptized into Jesus, and only later, when Peter and John come up and lay their hands on them, do they receive the Holy Spirit.) Act 18:24 And a certain Jew named Apollos, born at Alexandria, an eloquent man, and mighty in the scriptures, came to Ephesus.
Act 18:25 This man was instructed in the way of the Lord; and being fervent in the spirit, he spake and taught diligently the things of the Lord, knowing only the baptism of John.
Act 18:26 And he began to speak boldly in the synagogue: whom when Aquila and Priscilla had heard, they took him unto them, and expounded unto him the way of God more perfectly. Act 18:27 And when he was disposed to pass into Achaia, the brethren wrote, exhorting the disciples to receive him: who, when he was come, helped them much which had believed through grace:
Act 19:2 He said unto them, Have ye received the Holy Ghost since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
Act 19:3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
Act 19:4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
These people were WATER baptized but were not born of the Spirit...Not born again...No spiritual rebirth...
Act 19:5 When they heard this, they were baptized in the name of the Lord Jesus.
Act 19:6 And when Paul had laid his hands upon them, the Holy Ghost came on them; and they spake with tongues, and prophesied.
When these disciples were baptized the 2nd time, was there water involved???
Mat_3:11 I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:
John contrasts two baptisms here...One is with water, the other is with fire (and the Holy Ghost)...John did not say that Jesus will baptize with the Holy Ghost, water, and fire...
Baptism does not mean 'water'...Baptism means immersion...
In John's (water) baptism, no one received the Holy Spirit...John's water baptism was a symbol...A symbol that the person had repented/turned to Jesus...
At Pentecost, the apostles and disciples were not sprinkled or dipped before the Holy Ghost with cloven tongues of fire fell upon them...There is no mention of water in Acts 2:38...
I'm surprised when people turn to scriptures about faith or repentance, or confession of Christ when the question is about baptism.
You have to...They are intertwined...Baptism without faith and repentance would be meaningless...