I think Paul, for all the bashing he takes, planted the revolutionary seed that, if a master and a slave are both Christians, then doesn't that drastically change the relationship between them?
As for the slave he sent back, I believe he begs the owner to free him because he had become so dear to Paul.
Paul makes it pretty clear that the fleshly relationship of master/slave is far less important than that of being brothers in Christ.
You are correct that he asks Philemon to forgive and free Onesimus, his runaway slave, who apparently also stole items of value to finance his escape.
However, the important point is that there is not a hint in Paul's letter that slavery as an institution is wrong or unChristian.