The second question is purpose of the separation between Luke and the men described in verses 10-11:
10 Aristarchus my fellow prisoner greets you, and Mark the cousin of Barnabas (concerning whom you have received instructions—if he comes to you, welcome him), 11 and Jesus who is called Justus. These are the only men of the circumcision among my fellow workers for the kingdom of God, and they have been a comfort to me. 12 Epaphras, who is one of you, a servant of Christ Jesus, greets you, always struggling on your behalf in his prayers, that you may stand mature and fully assured in all the will of God. 13 For I bear him witness that he has worked hard for you and for those in Laodicea and in Hierapolis. 14 Luke the beloved physician greets you, as does Demas. Colossians 4:10–14 (ESV).
O’ Brien writes:
Luke and Demas add their greetings. Both names recur in Philemon 24 as Paul’s fellow-workers and at 2 Timothy 4:10, 11. Only here is Luke (on the name Λουκᾶς see BAG, 480) called “the beloved physician” (ὁ ἰατρὸς ὁ ἀγαπητός), and this has led to speculation that he was Paul’s doctor during his imprisonment. But there is no evidence for this. Luke’s profession was an unusual one so Paul mentions it, yet without further emphasis.
It is mainly on the basis of this verse, which separates him from Jewish Christians (οἱ ὄντες ἐκ περιτομῆς, v 11), that Luke was regarded as a Gentile Christian. Although this is possible, it is by no means certain, and if Ellis’ arguments above about “those of the circumcision” referring not to Jewish Christians generally but to one group within a twofold diaspora mission are correct, then it is possible he was a Hellenistic Jew (see E. E. Ellis, The Gospel of Luke NCB; London: Nelson, 1966) 52, 53; and note the comments above; Deissmann, Light from the Ancient East, 437, 438, favored identifying him with the Lucius of Rom 16:21).
Peter T. O’Brien, vol. 44, Word Biblical Commentary : Colossians-Philemon, Word Biblical Commentary (Dallas: Word, Incorporated, 2002), 256.