Which is described in Acts 2:38 and Acts 10:45.
No, Acts 2:38 is not the same as Acts 10:45, it is the same as Acts 10:48. Acts 10:45 corresponds to Acts 2:4.
This event placed them into the NT Church.
The same with the Gentiles...before their water baptism.
No, the coming of the Holy Spirit on them in the upper room did not put them into the Church. They were added to the Church when they were baptized (in water) into Christ (Gal 3:26).
Yes, I do, and you would too if you would read what Scripture says.
"While Peter was still speaking these words, the Holy Spirit fell upon all those who were listening to the message"
Peter had not yet told them to confess Jesus as Lord, he had not yet mentioned repentance, he had not mentioned baptism except for a reference to John's baptism. Cornelius had not done anything that Scripture says is a prerequisite to receiving salvation except hearing the Gospel preached. He had not yet "called on the Lord", so the Spirit falling on him was NOT indicative of salvation.
In Acts 4:4 the word "believed" is used to describe those who became Christians. Neither of what you wrote about is specifically stated. Thus, "believed" can be used as a synecdoche.
Absolutely, there are many places where only part of what is required to become a Christ follower is listed. Acts 2:38 is the closest to including everything and even it does not state it all in that one passage. For that very reason, passages like John 3:16 cannot be taken as meaning that all we have to do is "believe" (intellectual assent) to be saved. Every passage of Scripture that says something leads to salvation must be fulfilled in order to receive salvation. Thus, repentance, confession of Jesus as Lord, and baptism in water (the only three things that Scripture says "lead to salvation") must all be done or salvation is not received.
