Acts 4:5-12 King James Version (KJV)

5 And it came to pass on the morrow, that their rulers, and elders, and scribes,
6 And Annas the high priest, and Caiaphas, and John, and Alexander, and as many as were of the kindred of the high priest, were gathered together at Jerusalem.
7 And when they had set them in the midst, they asked, By what power, or by what name, have ye done this?
8 Then Peter, filled with the Holy Ghost, said unto them, Ye rulers of the people, and elders of Israel,
9 If we this day be examined of the good deed done to the impotent man, by what means he is made whole;
10 Be it known unto you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole.
11 This is the stone which was set at nought of you builders, which is become the head of the corner.
12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.

Acts 4:5-12 Amplified Bible (AMP)

5 Then on the following day, their magistrates and elders and scribes were assembled in Jerusalem,
6 Including Annas the high priest and Caiaphas and John and Alexander and all others who belonged to the high priestly relationship.
7 And they set the men in their midst and repeatedly demanded, By what sort of power or by what kind of authority did [such people as] you do this [healing]?
8 Then Peter, [because he was] filled with [and controlled by] the Holy Spirit, said to them, Rulers of the people and members of the council (the Sanhedrin),
9 If we are being put on trial [here] today and examined concerning a good deed done to benefit a feeble (helpless) cripple, by what means this man has been restored to health,
10 Let it be known and understood by all of you, and by the whole house of Israel, that in the name and through the power and authority of Jesus Christ of Nazareth, Whom you crucified, [but] Whom God raised from the dead, in Him and by means of Him this man is standing here before you well and sound in body.
11 This [Jesus] is the Stone which was despised and rejected by you, the builders, but which has become the Head of the corner [the Cornerstone].
12 And there is salvation in and through no one else, for there is no other name under heaven given among men by and in which we must be saved.

Amplified Bible (AMP) Copyright © 1954, 1958, 1962, 1964, 1965, 1987 by The Lockman Foundation

These are my thoughts, please share yours.

5-6 This shows that unlike with Christ they met during the day as they were required to do and perhaps it was not in secret as it was with Christ. It was not a secret trial as it was with Christ.

7 This is a good question for them to ask, because Satan has power and sometimes what Satan does may appear as good but with Satan it is always evil. Satan power leads to destruction but they were giving the message of hope, of Christ.

8 Being filled with the Spirit is important when giving His message that way you just become a mouth piece for Him, this is what happened with Peter. Peter shows them respect and it not bitter about the trial they had with Jesus. We can not allow our past to keep us from being used where God has brought us now. We can not win people to Christ by beating them down.

9 They were taken after helping the man, there mostly likely was a fear that their powers would be threatened again as they were when Christ was here. God is the one who should always have the power never those who serve Him; we gain power because He has granted it.

10 Peter now after getting their attention reminds them what they had done and tells them about Jesus. Peter gives the quick message of what happened to Christ and gives Him the credit for the man healing; those of the world would have take credit for themselves. Jesus’ name still holds power today.

11 Jesus is the chief cornerstone our faith is built on Him, a certain group of Christians see Peter as the rock the church was built on but it is our faith in Jesus that the church is built on. They rejected Jesus, Jesus will be rejected more times than accepted but at judgment all will call Jesus Lord but for to many it will be to late.

12 It is only by Jesus we are saved, no other name will be praised forever. It is by calling out from deep with in our heart to Jesus that we are saved, this is simply not speaking words but feeling a burden in our soul and is our soul crying out to Him. Jesus means the Lord’s salvation and that He is but He is so much more. Calling Jesus Lord is just words but for us to cry it from our souls to be saved causes a change to come over us and change that makes Him Lord.