Paul is on trial before Felix, the governor. "They" refers to the Jews. Paul says, "I confess," as he is giving testimony. He is a witness before a court, as he is on trial. "The way" is Christianity, which the Jews call a heresy.
"Believing all things which are written in the law and in the prophets" is really an astounding statement in light of what has gone on in Protestantism over the past few hundred years. The very man whom they say wrote most clearly and lucidly that "the law is done away" is the one who says he believes all things that are written in the Law and the Prophets. There is absolutely nothing in the Law and the Prophets that says anything at all about the doing away with God's law! Paul did not have the same position in relation to the law as modern theologians do.
One might think that maybe this was said before Paul wrote that the law was done away. Oh, no. The two books that contain most of what Protestants quote as their authority for doing away with the law are the books of Romans and Galatians. This instance in which Paul was on trial before Felix took place in either AD 58 or 59, most like the latter.
In either case, the book of Romans and the book of Galatians had both already been written. Both were being circulated through the church. All those doctrinal explanations were written prior to Paul's statement before Felix, yet Paul is still saying, "I believe all things that are written in the Law and the Prophets." Obviously, the common Protestant interpretation of Romans and Galatians is incorrect.
Certainly, salvation is by grace, but salvation in no way, of and by itself, does away with any of the law of God. Salvation is something that must be given. First of all, God's justice demands that there be a penalty for sin. Since His justice demands that the law be satisfied - that His own government be satisfied for crimes against it - He must follow through. He cannot wink at disagreements in a person's conduct against His rulership over His creation.
Secondly, once one of His laws has been broken, there is no way it can be undone. It has to be accepted according to what was done. Consider two simple examples of this:
If somebody is murdered, can that be undone? His life is gone. He is lying on the ground, dead. What is done is done. A person cannot resurrect him. The clock cannot be turned back. Nothing can be done to undo that act, unless there is a a power mightier than we are. So the law is broken. Another clear illustration might be a person's virginity. Once the virginity is taken away, or given away, it cannot be undone. The clock cannot be turned back. It is gone, never ever to be recovered.
The same is true with any act done, even when we are not considering law. However, we are considering law here, so we have to understand that it is God who has provided a solution for the breaking of law. What He has determined is to allow the death of Jesus Christ to pay the penalty, and then, in His mercy (called "grace" in the Bible), He will freely give the sinner relief from the penalty hanging over his head. We cannot make up for what has been done in the past. It can only be covered by a perfect sacrifice and God's willingness to accept that sacrifice.
If one studies the New Testament, and especially the writings of Paul, it is good to examine carefully the context in which the word "law" appears. Paul uses it very broadly. In fact, he uses the word "law" 110 times. Sometimes, he uses it to indicate a single law. At other times, he uses it to indicate the Mosaic law. There are other times when he uses it to indicate the Pentateuch, the first five books of the Bible. Yet at other times it refers only to the Ten Commandments.
A couple of interesting references are in Romans 2, where he uses "law" to indicate the will of God written in the hearts of Gentiles. Why Gentiles? Because they had not been given the law by God, yet he says they did the things contained within the law by nature. What it amounts to, in modern terminology, would be that he uses "law" in the sense of "natural law," that it is a standard that people consider to be in force without having been formally instructed by it. This became an issue, incidentally, in the confirmation of Clarence Thomas to the Supreme Court of the United States, because he professed to the Senate Judiciary Committee that he believed in natural law. The liberals on the Committee did not like that at all, because liberals like to be free of the constraints of natural law; they do not feel responsible then.
Another way Paul uses the word "law" is as if God Himself were speaking. He does not use the name or title of God, but the term "law," as in Romans 3:19. At times, Paul appears to contradict himself when he uses the word "law." In one place, he says, "Yea, we establish the law," but in another, he says, "Yea, we abolish the law." He uses it in the sense of it being both necessary and unnecessary. If one is careful, he will begin to become adept at figuring out how Paul uses it.
Paul's use of "law" appears in two general categories. If the subject of the context has to do with justification, then it is likely he will use a "no law" approach. That is both logical and right: No man can justify himself. All the lawkeeping in the world will not undo that murder or the loss of virginity. We cannot justify ourselves by what we do after we have broken a law. We cannot make up for it.
However, if the subject is sanctification - which has to do with a person's conduct, with right living, with discipline or character building - then Paul will say the law is valuable and necessary. It must be kept.
If we will just keep our eyes on the context, it will help us greatly to understand how Paul uses "law."
John W. Ritenbaugh
The Covenants, Grace, and Law (Part Seventeen)