Matthew 6:1-18 challenges much of what "church" does when we gather for public worship. There are three parts: one on giving, one on prayer, and one on fasting.
Those three parts are introduced by this one verse where Jesus says:
"Be careful not to practice your righteousness in front of others to be seen by them. If you do, you will have no reward from your Father in heaven." (Mt 6:1)The "you" and "your" in the scripture is PLURAL, not singular, so what Jesus is teaching isn't just about doing things in "secret" in the sense of being alone as one solitary individual. You can see this clearly in the beginning of the Lord's prayer where it's not "My Father" but "Our Father." Instead, it speaks to small groups of disciples (like the original 12) or the larger groups that met together for worship (such as in Acts and the Epistles) saying that they, as a group, should not make a show of giving or prayer or fasting (deprive ourselves of life's pleasures for a time so we can focus on the Lord) for the purpose of impressing any human beings. It's in secret FOR GOD and Him alone, not a show for those who happen to observe.
As to prayer in particular, Jesus' teaching about closing the door and not using many words speaks to the PURPOSE of prayer. The purpose of praying should not be (1) to put on a show for others or (2) because we think that God hears us better if we use many words. If we want to know about prayer and how this passage applies, we can look at the book of Acts and see how often the early disciples gathered... for prayer and life together. The first Christians had their own private prayer life, but it overflowed beyond to the gatherings of the faithful.
We can, and should, spend time alone in prayer, but there is no sense in scripture that prayer should be limited to that. Unfortunately the way most of us have experienced church life is that it's either (A) private prayer or (B) prayers for show, such as when prayers are prepared and carefully performed for a large gathering. The vision of the New Testament is of private, personal prayer WITH frequent times of praying to "our Father," praying for the coming of God's kingdom to us now, that all we do would be conformed to HIS will and not popular opinion, that OUR needs (daily bread for all) would be provided--often through sharing what we have (see James 1), that we would be overflowing with forgiveness and protected from sin and evil.
The Lord's prayer that is given here is a model prayer. It's not given to tell us we should always pray using these particular words. Luther and many other Bible teachers tell us this. We are to learn from this prayer about what topics and attitudes there should be in all our prayers. You'll notice, as you see all the other times when the disciples or early church prayed, that they used Jesus' teaching of this prayer to form how it was they would lift all their concerns to the Lord. And Luther was firm, someone reminded us the other night, that parents need to teach their children to pray. The way they learn that is by hearing the prayers of their parents and the other adults in their lives, prayers filled with joy and sorrow, prayers filled with praise and repentance, prayers for guidance and full of thanksgiving.
What Jesus says here doesn't mean we should never pray with many words, for Jesus himself prayed with many words (see John 17) as did the disciples (see Paul's letters and Acts). The point is that we should not do it to impress God or others
As to fasting, our Lord assumes we will deprive ourselves of worldly comforts for a time so we can focus on Him; but, again it's the attitude that matters. We don't do it to impress our parents, our children, our community, or anyone else.
In short, the idea that we should come to church so giving an offering or praying or other spiritual exercises can be performed for us is not what God has in mind. If we desire, as I hope we do, the spiritual rewards that come with spending time before the Lord, we will give and pray and fast as the disciples did--both as a group together, and alone with God. God has so much to give. Let's pursue it all so God's kingdom will come among us.