Well, what some call "conditions" are really manifestations.
Now, what in the world does that mean?
Faith is a gift (Php 1:29; 2Pe 1:1; Ac 18:27), by grace, through the new birth (Jn 3:5),
through which we receive the free gift of salvation (Eph 2:8-9).
All those things that some call conditions (obedience, perseverance, etc.) are really
the expressions (manifestations) of true faith, of a faith that is not dead, as James would say.
If these expressions (manifestations) of faith are not in our life, that shows (manifests) that
our faith is not true, it is counterfeit (Mt 7:21-23), we have not been born again.
If these manifestations are in our life, that shows that our faith is true,
because true faith obeys.
In fact, "belief" and "obedience" are the same word in NT Greek.
Yes, we are sons of God, not slaves of God.
"Purchased, bought back, redemption" are all OT terms of slavery used throughout the NT regarding what Christ accomplished on the cross for us in relation to God's justice; i.e., condemnation (Ro 8:1), God's wrath (Ro 5:9), eternal death, sin, etc.
Paul does not mean these terms as a description of our relation to God as our Father.
In that relationship, we are neither slaves nor servants, we are sons.