Yes, Jesus does require works to be saved.
He clearly stated in The Sermon on The Mount that in order to have our sins forgiven, we must first forgive others their trespasses. He also clearly stated if we do not forgive others The Father will not forgive us. Forgiveness of others is a righteous act we must perform to be forgiven by The Father.
Do not argue with me, argue with Jesus.
You are correct with understanding who Jesus was talking to, time period, culture, place and topic. All can provide us with clarity.
No Jesus wasn't promoting a legalistic system but was in fact providing a clear example of the law and how more than likely anyone who heard the Beatitudes saw their own imperfections. Which is the main idea behind most of Jesus's teachings. The law was Holy and perfect so by us taking what Jesus said in the Beatitudes and applying it to our lives, we would be acting from love as Jesus said if you love me you will keep my commands.
Jesus made a hard push to show the hypocrisy of the day by providing countless examples of how people just didn't measure up. The whole idea was to get them to understand the true role of the Messiah.
Matthew 5:17-20 New International Version (NIV)
The Fulfillment of the Law
17 “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.
Of course the Gentiles at first wasn't the main focus even though it had been prophesied and Jesus did in fact have many different occasions with Gentiles including 1 who he said had the greatest of faith. Or the woman at the well who he told to believe in him. When Peter first preached after receiving the Spirit, he was preaching to people from all over the known world including Gentiles. Many came to faith.
Paul was obviously more of a scholarly man so of course his teachings was often deeper and even hard for scholars today to agree on. But that doesn't prove anything. Paul and the Disciples taught the same Gospel. Paul was sent more to the Gentiles while the disciples mainly focused on the Jews but also spread out to the gentile world.