1:21 The NIV more literally translates this verse "to live is Christ" but the NRSV "living is Christ" perhaps better gets at the active, on-going tense of the infinitive verb here.
1:23 Paul uses the word "epithymia" for "desire" here, which he will elsewhere caution Christians against (make no provision for the flesh to gratify its desires...Romans 13:14)
1:25 The word for progress (prokopeh) here is precisely this, progress. Paul boasts in Galatians that he had progressed in his Judaism (1:14)
1:26 The word for Paul's visit is "parousia" is the word in the NT used for Jesus' second coming. The word can also mean presence (2 Cor 10:10)...or triumphal entry.
1:27 This verse has a KEY word: "politeuo-mai," which they translate as live. It literally means though, be a citizen. In Philippians Paul will describe a heavenly citizenship (3:20). This is foreshadowing of this.
1:27 Paul also commends people "in one spirit to fight/work together." (synathle-oo) In 4:3 he thanks God for the women who have done precisely this. More importantly, the root word here "athlew" is our word for athelete. Which today has connotations of merely sport, but here, it seems, Paul is emphasizing the public nature of Christian faith together. This links up well with 1:28 which talks about the public display of our faith.
1:30 Paul not only uses the word suffer (pasch-oo) in vs. 29 but also now uses the word "agon" (agony!) for struggle in vs. 30.