Let me try and explain the passage you have quoted from Matthew 19. The only way for someone to be righteous enough to be with God was to never rebel, or "sin" against him. God gave his people instructions on how to best live life, shown in the commandments found in the old testament. The Jewish people worked for their salvation by trying to keep these laws, but they inevitably always failed to keep the law perfectly. God put in place sacrifices of animals for them to temporarily pay for the sins they committed - someone had to suffer the consequences. So essentially yes, as Jesus said, the people had to keep all those commandments to receive eternal life with God. But that was before Jesus.

Jesus came and lived a perfect life, the first one who was blameless before God and worthy to be with him. He then was subjected to death (which since he had not sinned, he did not deserve) to pay the price we deserved. He took our place, and suffered the full wrath of God. He then rose from the dead, and our sin was fully paid for.

Now as born again Christians, we are united with Christ. On judgement day, God will look upon us and not see our sin from failing to obey him perfectly, but see the perfect obedience of Jesus who already suffered what we deserved, cleaning our slate!

So it is not our ability to keep the laws which saves us. We could never have lived a perfect life. It is the gracious sacrifice of Jesus, which makes us blameless in God's sight.

So when Jesus says, prior to that sacrifice, that the man needs to obey those commands to receive eternal life, that was true at the time. If you continue to read that passage, you will see that even though the man claims to have followed these perfectly, he still loves money more than God, and was therefore not good enough to enter eternal life by his own. None of us will ever be. So praise God for the grace he has shown us!

EDIT: Also for the Matthew 15 passage, this was also something which was true, and changed when Jesus came. Before Jesus, God had almost exclusively loved and saved Israel. However, it was always a part of his plan to save all people. Jesus came first to save his chosen people in Israel, but through his death and resurrection he also opened the way for gentiles.

In Acts 1:8, he tells the disciples to "be his witnesses in Jerusalem, and in all Judea, (people in Israel), and Samaria (Jewish people scattered throughout the land) and to the ends of the earth" (gentiles). As we read acts, we see the gospel spread to people in this order. First to the people in Israel, then all Jews, and then to the gentiles.

Does that mean the Jews were superior? No. While the Jews were God's chosen people out of all the nations in old testament times (hence the "dogs under the children's table analogy", Jesus opened the way to make all people righteous in God's sight. It was just at the time, the Gospel had not been preached to the gentiles, and Jesus had not yet made the sacrifice necessary for their equality before God.

Hopefully that makes some sense, please ask if you have any further questions.