Here I will address only the first of the OP's questions.  The second should be the subject of another question.

There is nothing unique or novel about the title "Son of God" for Jesus - it was revealed to Mary before His birth.  Below are listed numerous other occasions that people used this title for Jesus, many of which were before Peter's declaration in Matt 16:16.

 - Matt 8:29 - “What do You want with us, **Son of God**?” they shouted. “Have You come here to torture us before the appointed time?”
 - Matt 14:33 - Then those who were in the boat worshiped Him, saying, “Truly You are the **Son of God**!”
 - Matt 16:16 - Simon Peter answered, “You are the Christ, the **Son of the living God**.”
 - Matt 26:63, 64 - Then the high priest said to Him, “I charge You under oath by the living God: Tell us if You are the Christ, the **Son of God**.” “You have said it yourself,” Jesus answered.
 - Matt 27:43 - He trusts in God. Let God deliver Him now if He wants Him. For He said, ‘I am the **Son of God**.’”
 - Matt 27:54 - When the centurion and those with him who were guarding Jesus saw the earthquake and all that had happened, they were terrified and said, “Truly this was the **Son of God**.” See also Mark 15:39.
 - Mark 3:11 - And when the unclean spirits saw Him, they fell down before Him and cried out, “You are the **Son of God**!”
 - Mark 5:7 - And he shouted in a loud voice, “What do You want with me, Jesus, **Son of the Most High God**? I beg You before God not to torture me!”
 - Luke 1:35 - The angel replied, “The Holy Spirit will come upon you, and the power of the Most High will overshadow you. So the Holy One to be born will be called the **Son of God**.
 - Luke 4:41 - Demons also came out of many people, shouting, “You are the **Son of God**!” But He rebuked the demons and would not allow them to speak, because they knew He was the Christ.
 - Luke 8:28 - When the man saw Jesus, he cried out and fell down before Him, shouting in a loud voice, “What do You want with me, Jesus, **Son of the Most High God**? I beg You not to torture me!”
 - Luke 22:70, 71 - So they all asked, “Are You then the **Son of God**?” He replied, “You say that I am.” “Why do we need any more testimony?” they declared. “We have heard it for ourselves from His own lips.”
 - John 1:34 - I have seen and testified that this is the **Son of God**.
 - John 1:49 - “Rabbi,” Nathanael answered, “You are the **Son of God**! You are the King of Israel!”
 - John 3:18 - Whoever believes in Him is not condemned, but whoever does not believe has already been condemned, because he has not believed in the name of **God’s one and only Son**.
 - John 10:36 - then what about the One whom the Father sanctified and sent into the world? How then can you accuse Me of blasphemy for stating that I am the **Son of God**?
 - John 11:4 - When Jesus heard this, He said, “This sickness will not end in death. No, it is for the glory of God, so that the **Son of God** may be glorified through it.”
 - John 11:27 - “Yes, Lord,” she answered, “I believe that You are the Christ, the **Son of God**, who was to come into the world.”
 - John 19:7 - “We have a law,” answered the Jews, “and according to that law He must die, because He declared Himself to be the **Son of God**.”

That is, Jesus was often addressed as "Son of God"before His resurrection from the dead, with many of these occasions before Peter's declaration in Matt 16:16.