Matthew 5:13-48

2) Jesus defines our identity. He was talking to His disciples " ... You are the salt of the earth.... you are the light of the world..." Salt never loses its saltiness. The Greek word for tasteless (moraine) can mean to become foolish - in this context, it means becomes flat, losing its true purity and essence. So the application here is be salt, stay salty ;)

Light of the world means be a big beacon of light for Jesus. Don't hide it! "Let your light shine... that they may see your good works and glorify your Father Who is in heaven." I John 1:5-7, Eph 4:6-14 If you are truly transformed and have faith in Jesus, you cannot be living lives in the opposition direction of being a salt and light for GOD.

When I was a in Sunday School, I used to sing this song:

This little light of mine,I'm gonna let it shine

This little light of mine,I'm gonna let it shine

This little light of mine,I'm gonna let it shine

Let it shine,Let it shine,Let it shine.

Hide it under a bushel? No!I'm gonna let it shine

Hide it under a bushel? No!I'm gonna let it shine

Hide it under a bushel? No!I'm gonna let it shine

Let it shine,Let it shine,Let it shine.

3) Jesus defines the Law and its applications Matt 5:17-47. In this portion of the text, we see quite a few of "You have heard but I say to you" - Jesus was telling His disciples that you have heard the views of the world but I say to you the system of the kingdom of heaven is different, dealing with sin in a different manner. For e.g. the OT teaches us that "You shall not murder" - Jesus reveals the real intent of what it really meant, He drives it deeper to see what is in the heart. Another e.g. is "You shall not commit adultery" - Jesus says that everyone who looks at a woman with lust for her has already committed adultery! It is important to note in v. 17 that Jesus said I did not come to abolish the Law or the Prophets but to fulfil it.
V.38-42 talks about Restitution or Revenge. Jesus is saying, while it is our legal right to be compensated for the wrong doings others have committed against us, we can also exercise forgiveness and give up that right for restitution so that your "righteousness surpass that of the Scribes and Pharisees" v. 20.

Finally, Matt 5: 48 ended with "Therefore you are to be perfect, as your heavenly Father is perfect." Perfect refers to "Teleios" - complete, mature; wanting nothing necessary to complement. Lev 19:2, Deut 18:13, I Pet 1:13-16.