1:1 Paul, called as an apostle of Jesus Christ by the will of God, and our brother Sosthenes, [NASB]
My commentary:
1) Only Paul was "called" (invited to be) an apostle. This refers to the Damascus Road Encounter.
2) Yes, part of the requirements of being an Apostle of Christ is to be an Ambassador of Christ, But all born anew believers are Ambassadors, but we are NOT Apostles, chosen by Christ and eyewitnesses. (Paul was an eyewitness of a visible manifestation of Jesus after Jesus had ascended.)
3) Yes, God chose Paul, after Paul "called on the name of the Lord" for salvation and as an Apostle.
4) Yes, Paul was "set apart" to present the gospel of Christ to the Gentiles.
And here are my comments on your paraphrase.
1) Well done! Part of actual bible study is to put our understanding of the meaning in our own words! This allows us to crosscheck our understanding with other verses presenting a similar message to see if our view is consistent with all scripture.
2) No, to be an Apostle carries a greater designation than to be an Ambassador. We present what the Apostles presented, like the difference between prophets and teachers.
3) Yes, Paul mentions his communication is not only from him, but also from fellow workers, in this case Sosthenes.