This passage is a mix of good things about people and some problems Jesus has for us to consider before we start on his positive teaching in the next passage.
First there is the story of the call of Levi and a strong suggestion that what he did was good. Then two more stories in which Jesus was challenged over the things he did that people thought he should not do:
Finally Luke gives us the complete list of the Apostles.
First Jesus was eating with those with whom one should not eat - according to those we will call 'the serious' because they were serious about their religion. We read Luke 5:27-32: eating with those with whom one should not eat!
Levi seems to be the same person called Matthew in the other gospels and therefore the person who wrote what we call Matthew's Gospel.
This is not a call to follow a system, a philosophy, or a religion. It is a straight call to follow one person: Jesus. The true call to discipleship is just the same today. There are many half-hearted Christians in the world today. A good question for them is "do you follow Jesus?".
Luke recognises that, for Jesus, life and faith were all about including people in as much as possible rather than turning them away as not good enough, not learned enough, not old enough - anything else for which people are 'not enough'. Doing that still upsets people who consider themselves serious in matters of religion!
In the next story Jesus did not argue against the principles of the Law of Moses but against all the many little rules that people had added to it. He knew that if people are given many rules they will forget the greater principles they should be thinking about. So concern for all these detailed rules would hide the new things he was teaching, particularly those relating to the work of the Spirit. The challenge to us is to identify which of our rules, written or unwritten, get in the way of what we should really be doing. All too often we continue to do the things that our parents and grandparents decided were the right things to do when they were young. But the world we are living in is changing all the time, perhaps faster than it has ever done before. The things that are not part of the necessary centre of our faith may need to be changed. Jesus explains that in some very vivid and exciting short sayings.
Read Luke 5: 33 - 39 : eating when one should not eat!
The answers to both this and the next question are going to depend very much on your circumstances.
Jesus said "the old wine is better". He is being sarcastic. He knows many think old things are better than new things as old wine is better than new wine but he is challenging his followers to new and better things.
The last two stories Luke 6: 1 - 5 and Luke 6:6-11 are both about Sabbath keeping. The Sabbath was the Saturday religious day of the Jews. The early Christians changed their day of celebration to Sunday, the first day of the week, in memory of the resurrection of Jesus. This was one of the three things (keeping the food laws, Sabbath keeping, circumcision) Jews of that time did to show that they really were the people of God.
We read Luke 6: 1 - 11: doing what one should not do!
Micah, an Old Testament prophet said "what does the Lord desire of you? To act justly, and to love mercy and to walk humbly with your God" and said that the Lord did not want offerings and sacrifices. Although Jesus never actually quoted those words he often alluded to them.
Read Luke 6: 12 - 16.
Of those 12 men only one, John, is certainly known to have died of old age. Peter was crucified upside down (because he did not want to be crucified the same way up as Jesus) in Rome, Thomas probably got the furthest and was killed in south India, the rest died here and there in the ancient world as they proclaimed the good message of Jesus.