You serious?
1. Peter was speaking of those Jews who were living in a foreign land which was not their own, as these were considered as "exiles", as the Greek has it.
Your going to have to do more than make assertions without historical or Scriptural proof. There is not anything that I know that supports your thinking that Peter was writing to the Jews.
Rather, the evidence is that he was writing to the church, and as the church the folks were alien in this world.
2. Where does it say here, that these were "chosen" to salvation? I doubt very much if ALL these Peter writes about here, were "the elect" of God. All he is here referring to, is that the Jews had a special relationship with God.
I quoted you Scriptures. It is truly sad that you have so little insight into the Scripture presented that you would discard it with words such as "I doubt" and "All he is here referring to." Especially, when you are mistaken.
Here is a link that will give you at least a tiny bit of insight:
An Introduction To The Book Of 1 Peter
3. The Greek preposition, "εἰς", here translated "to" obey, is also used as "because of", as in Jesus saying that the people of Nineveh repented "εἰς", because of, the preaching of Jonah (Matthew 12:41). also in Acts 2:38, "Peter replied, "Each of you must repent of your sins and turn to God, and be baptized in the name of Jesus Christ for (εἰς, because of) the forgiveness of your sins. Then you will receive the gift of the Holy Spirit.". No sinner is saved by water baptism, but because they had truly repented.
Either you are not taking is matter seriously, or you have difficulty carrying the topic through the passage.
What is presented in 1 Peter 1:3-5:
3Blessed be the God and Father of our Lord Jesus Christ, who
according to His great mercy has caused us to be born again ...
It is the Father who extends "His great mercy" and CAUSED us to be born again. Peter supports election and irresistible grace.
...to a living hope through the resurrection of Jesus Christ from the dead,
4t
o obtain an inheritance which is imperishable and undefiled and will not fade away, reserved in heaven for you,
5who are protected by the power of God through faith for a salvation ready to be revealed in the last time.
The resurrection from the dead provided that inheritance and that inheritance is imperishable, undefiled, and will not fad away. To that end the believer has such an inheritance reserved in heaven, are protected by the power of God and that the salvation (ultimate reward for believers) is being readied to be revealed.
This is, as you agree, a presentation of perseverance and preservation of the saints.
Here is a companion passage from Ephesians 1. It is commonly used to also show the same areas in agreement with 1 Peter. It is not necessary for me to point out specifically that areas, but I will highlight some that you see the evidences of the Doctrines of Grace expressed in the writing of Paul, also:
Ephesians 1:
1Paul, an apostle of Christ Jesus by the will of God,
To the saints who are at Ephesus and
who are faithful in Christ Jesus:
2Grace to you and peace from God our Father and the Lord Jesus Christ.
3Blessed
be the God and Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in the heavenly
places in Christ,
4just as
He chose us in Him before the foundation of the world, that we would be holy and blameless before Him. In love
5He predestined us to adoption as sons through Jesus Christ to Himself, according to the
kind intention of His will,
6to the praise of the glory of
His grace, which He freely bestowed on us in the Beloved.
7In Him we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace
8which He lavished on us.
Now, it is past time that I leave this thread for a bit.
I trust you will come to understand that the position of the Doctrines of Grace is not foreign to the Scriptures, but is by far that which represent the truth of the matter, far more then any other presentation.