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).
ἀσπάζεται ὑμᾶς Λουκᾶς ὁ ἰατρὸς ὁ ἀγαπητὸς καὶ Δημᾶς. The last two to be included in the list of greetings are Luke and Demas, who again are mentioned together with Epaphras, Mark, and Aristarchus in Phm. 24. Luke is also mentioned on one other occasion in the New Testament, in 2 Tim. 4:11 (“Luke alone is with me”), though there again Mark and Demas (also Tychicus) are named in close proximity (2 Tim. 4:10–12). The present passage contains the only firm information about Luke, that, apart from being a close companion of Paul’s (at least during his later imprisonment), and one of Paul’s “coworkers” (Phm. 24), he was a doctor. That indicates a man of some learning and training (though at this time medicine was only just becoming a subject of systematic instruction; see OCD, “Medicine” 662). And since the title has a favorable ring here (contrast the typical criticism of doctors elsewhere in biblical tradition: 2 Chron. 16:12; Job 13:4; Jer. 46:11; Mark 5:26) we may assume that he was no charlatan but respected for genuine medical knowledge and healing skills. Beyond that we know nothing firm about Luke, though there is of course the long-established tradition that the Luke mentioned here was a regular companion of Paul in the main phase of his missionary work (the “we” passages in Acts) and the author of Luke-Acts (so particularly Eusebius, Historia Ecclesiastica 3.4.1–7; 3.24.14–15; 5.8.3; 6.25.6). The same traditions speak of Luke as an Antiochian (3.4.6), and others claim that Paul wrote Hebrews in Hebrew/Aramaic, which Luke then translated into Greek (3.38.2; 6.14.2). He has also been identified with the Lucius of Rom. 16:21 (e.g., Martin, Colossians and Philemon 136; but see Lightfoot 239). The note of affection here (ὁ ἀγαπητός, “dear friend” in JB/NJB, NEB/REB, NIV) indicates a closeness of relationship with Paul, a quality of friendship shared with Epaphras, Tychicus, and Onesimus (1:7; 4:7, 9).
James D. G. Dunn, The Epistles to the Colossians and to Philemon : A Commentary on the Greek Text (Grand Rapids, Mich.; Carlisle: William B. Eerdmans Publishing; Paternoster Press, 1996), 282-83.