18:7 He departed there, and went into the house of a certain man named Justus,
one who worshiped God, whose house was next door to the synagogue. 
18:8 Crispus, the ruler of the synagogue, believed in the Lord with all his house. 
Many of the Corinthians, when they heard, believed and were baptized. 
18:9 The Lord said to Paul in the night by a vision,
"Don't be afraid, but speak and don't be silent; 
18:10 for I am with you, and no one will attack you to harm you,
for I have many people in this city." 
18:11 He lived there a year and six months, 
teaching the word of God among them. 

18:12 But when Gallio was proconsul of Achaia,
the Jews with one accord rose up against Paul 
and brought him before the judgment seat, 
18:13 saying, "This man persuades men to worship God contrary to the law." 
18:14 But when Paul was about to open his mouth, Gallio said to the Jews, 
"If indeed it were a matter of wrong or of wicked crime, 
you Jews, it would be reasonable that I should bear with you; 
18:15 but if they are questions about words and names and your own law,
look to it yourselves. For I don't want to be a judge of these matters." 
18:16 He drove them from the judgment seat. 
18:17 Then all the Greeks laid hold on Sosthenes, the ruler of the synagogue,
and beat him before the judgment seat. Gallio didn't care about any of these things. 
 

The church in Rome was not founded by the Apostle Peter nor by Paul, but probably by Priscilla and Aquila or the like. It is unusual for wife's name to come first, but this is likely a sign of the difference in social status between the two. Aquila may have come from a slave class but was redeemed by Priscilla, a rich Jewess. 

vs 3 The Christian community today has taken up the term "Tentmaker ministry", referencing Paul's ministry which is not likened to that of a fulltime profession Christian minister, but rather of that of the ordinary Christian working at at secular job along with doing ministry as well. Such serves as an example to ordinary Christians today, and no doubt to the couple he was staying with as well.

vs 4 It is interesting the it doesn't say that he "preached", but rather that he "reasoned". Preaching most often has to do with transferring information. But reasoning is more about convincing based upon the given information. For Jews were familiar with the scriptures and no doubt aware of the historic facts associated with Jesus Christ. But what to do with that information is a matter of reasoning. Christian faith is not a blind faith. Christian faith is a reasonable faith. Evangelism is not simply about telling. It's also about convincing and persuading.

vs 5 It is apparent that before he assembled his team of Silas and Timothy, Paul had decided not to directly confront them with propositions as to who Jesus was, but rather probably tried to prepare them by focussing on issues like conviction of sin and the idea of the forgiveness of sins and humility and such, just as Jesus had in his ministry before revealing himself. Leading people to Christ is not a point in time event. Leading people to Christ is leading them along the straight and narrow road. Yes, it can end with a point in time event in which they put saving faith in Christ, but we need to think in terms of the process of getting them to that point. Notice also that Paul was guided by his spirit as to when to present what to them. He was pressed in spirit. That's how he was guided in this matter. Do you feel pressure in your spirit to act upon something? Perhaps you are being guided by the Spirit to do so.

vs 6 Let us not become complacent nor intimidated at the threat that those we attempt to influence may end up rejecting us and our message, and even with hostility. Nor let other onlookers mock us as if failures. For this is the normal experience in ministry one should expect as we see reflected in the ministries of Jesus and Paul. And may I say that American Evangelicalism is too obsessed with popularity. But what should be the Christian response to such hostility? Primarily just to move on. 

It seems what drove Paul was primarily the sense of responsibility to fulfill the commission given him by the Lord. We see this many places in his letters. 

Rom 1:1 "Paul, a servant of Christ Jesus, called to be an apostle and set apart for the gospel of God--"
Rom 1:14 "I am obligated both to Greeks and non-Greeks, both to the wise and the foolish."
1Cor 9:16,17  "Yet when I preach the gospel, I cannot boast, for I am compelled to preach. Woe to me if I do not preach the gospel! If I preach voluntarily, I have a reward; if not voluntarily, I am simply discharging the trust committed to me."
Col 1:25  "I have become its servant by the commission God gave me to present to you the word of God in its fullness"

"Your blood be upon your own heads" simply means that they will be held  responsible for their sins and that having rejected Christ, the atoning sacrifice for their sins, they have no redeemer and will have to pay the penalty for their own sins.

vs 7 It is apparent by the way he is spoken of that Justus was a God-fearing Gentile much as Cornelius of Chapter 10. The fact that his house was physically joined to the synagogue indicates to me that he had been God-fearing for a while and devoted to helping the Jewish community, which was no doubt how he came into contact with Paul.

vs 8 Despite the fact of verse 6 implying that the majority of Jews rejected him, and that he decided to focus his ministry upon the Gentiles, yet realize that he had as a convert a well respected Jewish leader, Cripus and his household, who though being the chief leader of the synagogue at the time, such a position was no doubt taken from him some time after this event as we see in verse 17 that another took his place.

vs 9-10 Another thing to realize when facing hostility is that there may be more people empathic to your cause than is apparent. Hostile people make alot of noise and try to give the impression that the mob supports them. The righteous, not tending to be so loud and boastful, but are more reflective of a still gentle voice, may not stand out so much.  I am reminded of Elijah who under persecution said to God, "I am the only one left, and now they are trying to kill me too." But part of God's reply was, "I reserve seven thousand in Israel-- all whose knees have not bowed down to Baal." There are alot more Christians out there of like heart than we may realize.

It's also interesting that there seems a correlation between "for I have much people in this city" and "no man will harm thee." God affirms that Christians are logically safer in places where there are alot of righteous people. But what this also implies is that those areas in which Christians suffer much persecution, God does not have many of his people there. The population is dominated by the unrighteous. What does this say today of about those areas dominated by the Islam, in which Christians face a great deal of persecution? Or areas dominated by communism? But what this implies also is a degree of the freedom of the will in which if a society is dominated by the unrighteous, God allows them the freedom to express their unrighteousness, for which of course they will be held accountable. And that is God's sovereignty. This as opposed to a puppet model of God's sovereignty.

vs 11 Again we get a sense of the time frame Paul ministers in a given area. Most frequently it is between one and three years, much as is reflected in the Lord's ministry as well. Much as Paul reckoned his ministry to be one of a planter rather than a waterer, yet we note that he does spend a good deal of time in teaching the word and not simply preaching a message and moving on. If people respond, then he spends time with them. 

vs 12-17 It is apparent the Jews were unaware of the antisemitism of Greek society against them. The governor's attitude is not surprising, being a Roman official. For as we noted in the beginning of the expulsion of the Jews from Rome. But really his response is not much different than that of Pilate, only at this point the Jews had no political clout in Roman society to get their way. The Jews may have tried to make the point that they were speaking of Roman law, of which they may have in fact had a point. For Christianity was not a recognized religion and as such was illegal under Romans law. But Gallio simply refused to hear them further and no doubt the Greeks who went on to persecute the Jews were aware of his antisemitic attitude. But it is interesting that they didn't persecute Paul. For he may have been viewed more sympathetic to the Gentiles, having identified with the god-fearing Gentiles and rejected the unbelieving Jews. But he certainly didn't seek for nor condone the antisemitic attitude of those who persecuted Sosthenes.