Peter's second speech in the Temple

On Pentecost, Peter made the first kerygma outside the Temple. Who were the audience? Luke painstakingly painted a universal picture.
Parthians and Medes and Elamites and residents of Mesopotamia, Judea and Cappadocia, Pontus and Asia,
Phrygia and Pamphylia, Egypt and the parts of Libya belonging to Cyrene, and visitors from Rome, both Jews and proselytes,
Cretans and Arabians, we hear them telling in our own tongues the mighty works of God (Acts 2:9-11).
But when he began to speak, Peter addressed the crowd "Men of Judea and all who dwell in Jerusalem" (Acts 2:14). Later, he called them "Men of Israel" (Acts 2:22). In the end, he intimately called them "Brethren".
Did Peter speak only to a subset of this cosmopolitan crowd? If affirmative, how did the remaining crowd hear him? Did the other disciples instantaneously translate Peter's speech to the rest of the crowd? And was "men of Israel" a larger audience than "men of Judea"? I think this is an interesting topic for Biblical students to pursue.

Let's return into the Temple. After healing at the Beautiful Gate, the lame man followed Peter and John into the Temple, praising God on the way. Another crowd gathered around Peter and John in Solomon Portico and Peter began his second kerygma, addressing them as "Men of Israel" (Acts 3:12). He pointed out that they had denied Jesus, the Holy and Righteous One and the Author of Life. Now the lame man stood healed through the faith in Jesus in front of them all.
And his name, by faith in his name, has made this man strong whom you see and know; and the faith which is through Jesus has given the man this perfect health in the presence of you all (Acts 3:16).
Peter had borne witness to Jesus. He was not just Lord and Christ (Acts 2:36), but the Author of Life (Acts 3:15). Not only was Jesus raised from the dead, but he also gave life, a full and healthy life.

Then Peter spoke intimately again and addressed them as "brethren". He understood them and made excuse for them. They denied Jesus out of their ignorance. It was a friendly gesture in order to win them over (Acts 3:17). Here came his advice.
Repent therefore, and turn again, that your sins may be blotted out, that times of refreshing may come from the presence of the Lord,
and that he may send the Christ appointed for you, Jesus (Acts 3:19-20).
Repent and have sins forgiven. I understand. Receive Jesus and obtain life. I understand. But what does "times of refreshing" mean? Biblical students. Here is another topic for you to research.

Before you leave, I suggest you taking a look at the following appendix. Luke was quoting the Torah in Greek. This time, the wording was not a word-for-word transcription from the Septuagint like he did in the first kerygma. Luke seemed to have paraphrased instead. Why? I have no satisfactory explanation yet. More comparative analysis is needed.

Dear Lord, let us be more considerate and sympathetic in conveying Your message to our neighbour. Amen.

Appendix:
Moses said, 'The Lord God will raise up for you a prophet from your brethren as he raised me up. You shall listen to him in whatever he tells you.'
Μωϋσῆς μὲν εἶπεν ὅτι προφήτην ὑμῖν ἀναστήσει κύριος ὁ θεὸς ὑμῶν ἐκ τῶν ἀδελφῶν ὑμῶν ὡς ἐμέ· αὐτοῦ ἀκούσεσθε κατὰ πάντα ὅσα ἂν λαλήσῃ πρὸς ὑμᾶς. (Acts 3:22)
προφήτην ἐκ τῶν ἀδελφῶν σου ὡς ἐμὲ ἀναστήσει σοι κύριος ὁ θεός σου, αὐτοῦ ἀκούσεσθε 
κατὰ πάντα, ὅσα ᾐτήσω παρὰ κυρίου τοῦ θεοῦ σου ἐν Χωρηβ τῇ ἡμέρᾳ τῆς ἐκκλησίας λέγοντες Οὐ προσθήσομεν ἀκοῦσαι τὴν φωνὴν κυρίου τοῦ θεοῦ ἡμῶν καὶ τὸ πῦρ τὸ μέγα τοῦτο οὐκ ὀψόμεθα ἔτι οὐδὲ μὴ ἀποθάνωμεν, (Deuteronomy 18:15-16).
And it shall be that every soul that does not listen to that prophet shall be destroyed from the people.
ἔσται δὲ πᾶσα ψυχὴ ἥτις ἐὰν μὴ ἀκούσῃ τοῦ προφήτου ἐκείνου ἐξολεθρευθήσεται ἐκ τοῦ λαοῦ. (Acts 3:23)
καὶ ὁ ἄνθρωπος, ὃς ἐὰν μὴ ἀκούσῃ ὅσα ἐὰν λαλήσῃ ὁ προφήτης ἐπὶ τῷ ὀνόματί μου, ἐγὼ ἐκδικήσω ἐξ αὐτοῦ.(Deuteronomy 18:19)
And in your posterity shall all the families of the earth be blessed.
καὶ ἐν τῷ σπέρματί σου [ἐν-]ευλογηθήσονται πᾶσαι αἱ πατριαὶ τῆς γῆς. (Acts 3:25b)
καὶ ἐνευλογηθήσονται ἐν τῷ σπέρματί σου πάντα τὰ ἔθνη τῆς γῆς, ἀνθ̓ ὧν ὑπήκουσας τῆς ἐμῆς φωνῆς.(Genesis 22:18)