Q: "Why does Paul mention James before Peter (Galatians 2:7-9) and why is Peters' name used as "Cephas" instead sometimes?"

 Firstly, if the hidden assumption behind the question here is, “Any name mentioned first in a list of names necessarily means that the person holding that name mentioned first is superior to all others in that list” then we should recognize that the assumption is not always true. Now, of course, Peter’s name is mentioned first when it comes to the listing of apostles, and that’s a case to be made for his superiority among the apostles. But, this type of conclusion is made with (1) the additional biblical and historical data that shows Peter was in fact the leader of the apostles, and (2) the fact that Peter is consistently mentioned first not only one time, but many times over and over, making it more likely.

Second, I want to recognize that this is a good question, and we can actually see the logical pattern as to how Paul lists the four people (me [Paul], James and Cephas and John), as opposed to being merely random. But before that, it is important for us readers to recognize that Paul is writing Galatians primarily to address the Judaizers, who wanted new Christians to be forced to be circumcised, otherwise they are not Christians; Paul and the rest of Christendom rejects this notion of having to be circumcised in order to be Christian. Ok, back to what I was saying, Paul lists from the most important figures pertaining to this Judaizer conflict to the least important figures, respectively. Paul, is the writer and is a Pharisaic Jew who was born in the law (Phil. 3:5) and is the one who rebukes Peter, the leader of the apostles (Gal. 2:11), so he is most fitting to sympathize with the Judaizers zealous for the law of circumcision being so concerned with the truth. I will address James and Cephas later, but for now, look at John. Why is John last? Well, I think it actually has to do with his age. Tradition and scholarship have generally accepted that he was the youngest out of the original twelve apostles of Jesus. And so it would make sense he is after everyone. Moreover, John is always listed after his brother James elsewhere in the NT, so that would make more sense as to why John is after James here.

Prior to reading any Bible commentaries, I suspected the answer to your first question had something to do with James being in Jerusalem (which was a very Jewish place) and those to whom Paul, the author of Galatians, is addressing, namely, the Judaizers (who are Jews). And that’s correct.

Here’s what A Catholic Commentary on Holy Scripture (probably the best Catholic commentary on scripture out there, according to my knowledge) says, “...when St Paul is speaking of the missionary office of the Church at large, St Peter holds the foremost place [“foremost” meaning being mentioned first], 7, 8: when he [Paul] refers to a special act of the Church of Jerusalem, St James is mentioned first, as here; cf. Ac[ts] 12:17; 15:13; 21:18.” 

Basically, James is mentioned before Peter because he himself was an important Jewish figure for Paul (writing Galatians) to use while teaching these Judaizers (who are Jewish) while Peter is probably away from Jerusalem (Acts 12:17). It would be more convincing to have an important figure who is close to you to convince you of something than having another important figure who is far from to to convince you of something.

Now, to your second question, why is Peter’s name used as “Cephas” in some places and “Peter” in other places in Galatians? Maybe, the answer is that Paul wanted to show the progression of authority for Paul to teach the Judaizers. Firstly, the name Peter is not as authoritative as Cephas. “Cephas” in Aramaic means “Rock,” and so would’ve been closer to the usual language of Jesus, who is most authoritative. And “Peter” in Greek also means “Rock,” but the language is likely not Jesus’ usual language. So basically the name which is given to Peter/Cephas that is closer to Jesus’ usual language would be more authoritative. Ok, I want you to notice that “Peter” is used twice before the listing of “Cephas” and others. Notice that just right before verse 11, where Paul rebukes Cephas, Paul sneaks in Peter’s name as being Cephas instead. What I suspect Paul is doing is that he is preparing for the rebuking of Peter in verse 11. It is important for Paul to exaggerate Peter as this strong and authoritative leader as being called “Cephas” of the original Aramaic language of Jesus firstly, and then rebuke that same strong and authoritative leader called “Cephas” later on. Why? Paul wants to show that he is *MORE* concerned with the truth than authority. So even though Peter has more authority than all the apostles, including Paul, Paul will rebuke Peter if Peter goes wrong. Likewise, any leaders among the Judaizers who dares to push false Judaizing practice will get the same treatment from Paul, despite being leaders. Thus, Paul’s argumentative case against the false practices of the Judaizers are strengthened.

By the way, *A Catholic Commentary on Holy Scripture is freely available on Verbum and also on LogosBible, two apps that are downloadable.