Fortunately the answer to both these questions is the very same thing. In fact, that is at the essence of what Lutherans believe about all matters of doctrine: Lutherans believe what Scripture teaches; no more and no less. Now there are various competing interpretations out there in Christendom, yet I would argue that in consideration of the full counsel of Holy Scripture on Baptism (and also the doctrine of the Holy Spirit, which is tied to this), these other interpretations are either incomplete (certain passages are not considered), or they simply disregard the text.
For your reference I have compiled every instance of how “Baptism” or “Baptize” appears in the Greek: Baptism Verses (forgive me if I missed one unintentionally)
Baptism is “instituted” by Christ in Matthew 28:18-20:
18And Jesus came and said to them, “All authority in heaven and on earth has been given to me. 19Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, 20teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”
This is commonly known as the Great Commission and the command here is “make disciples” (note it is not “go”). “Baptizing” and “teaching” are both the means by which this command is carried out. Both go together, you don’t do one and not the other. “All nations” should be understood in the context as literally everyone without exclusion. This is especially important as Matthew’s Gospel presents Jesus as Israel reduced down to one… everyone else is a goy… that is a Gentile… or part of “the nations” (the word that is used for Gentile and nations are the same). If the word for “nations” is also understood by its derivative theological meaning of “heathen” or “pagan”, which again in the context of Matthew’s Gospel where a big theme is bringing outsiders into the inside, then Baptism certainly may precede a public profession of faith (as in the case of infants).
The next time, chronologically, we have this word pop up is in Acts 1 & 2. The first is in Acts 1:5, that the disciples would be “baptized with fire” in contrast to John’s baptism with water (note this does not discount that the Baptism Jesus spoke about in Matthew 28 was intended to be understood with water and in the Name of the Father, Son, and Holy Spirit). We then see this fulfilled in the narrative in the very next chapter where flames rest on the apostle’s and they speak to the various “nations” that are present for the feast of Pentecost. Peter preaches, the people are cut to the heart and ask, “What shall we do?” (Acts 2:37) and Peter responds, “Repent and be baptized [passive imperative] every one of you in the name of Jesus Christ for the forgiveness of your sins and you will receive the gift of the Holy Spirit. For this promise is for you and for your children and for all who are far off, everyone whom the Lord calls to Himself” (Acts 2:38-39). Here Peter says a lot in just two verses. First, Baptism [and repentance… again, the two go hand in hand] is “for the forgiveness of sins”. Second, Baptism is in the name of Jesus Christ. This does not contradict Jesus institution in Matthew 28, but is a linguistic shorthand called a synecdoche (kind of like saying, “hey check out my new wheels”, you mean for the person to look at your whole car… at least usually). Third, Peter calls Baptism a “promise” and this “promise” is for the hearers… but not only them but for those who aren’t there as well (the ones who are far off)… and for their children! A promise is received by faith… by trust. The thing that makes a promise certain or uncertain is who makes the promise. With God, His promise is as sure as a done deal.
Peter also speaks of Baptism in his first Epistle in 1 Peter 3:21: “Baptism, which corresponds to this, now saves you, not as a removal of dirt from the body but as an appeal to God for a good conscience, through the resurrection of Jesus Christ.” The main clause (Subject-verb-object) here is “Baptism saves you”. In the context, Peter says Noah and his family passing through the flood and being saved in the ark is a foreshadow, a “type”, which points forward to Baptism. How can Baptism do such great things as save a person? Well it isn’t a mere removal of dirt from the body (like taking a shower), but Baptism (which Peter treats here as a noun, a thing) is “an appeal to God for a good conscience”. This phrase is loaded with court language. The image here is Christ standing in as our defense attorney pleading our case. What case does Christ make? He points to His resurrection.
What Peter alludes to here, Paul makes very clear in Romans 6: “3Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? 4We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life. 5For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his.” Paul says here Baptism does something more, it unites us to Christ’s death and resurrection. In this we die with Christ and rise again to new life. This is what Lutherans mean when we talk about the “old Adam” dying. In a sense, Baptism delivers the Resurrection to us right now, even though it’s “end” (telos) is seen finally in the Resurrection.
Finally, one more passage to bring forward is Titus 3:4-8: “4But when the goodness and loving kindness of God our Savior appeared, 5he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit, 6whom he poured out on us richly through Jesus Christ our Savior, 7so that being justified by his grace we might become heirs according to the hope of eternal life. 8The saying is trustworthy, and I want you to insist on these things, so that those who have believed in God may be careful to devote themselves to good works. These things are excellent and profitable for people.” This is a bit of a long passage, and I admit, while the word for Baptism is not explicitly used, Paul alludes to it here in the word “washing.” In all of Scripture this word is used only here and in Ephesians 5:26, “the washing of water with the word.” This is precisely what Baptism is! Water… with the word. If one concedes this is the case (which I won’t argue further here for sake of “brevity”), then back to Paul’s words in Titus: God our Savior saved us according to His mercy through (by means of: “dia” + the dative in the Greek is a dative of means/instrumental causation) this washing of regeneration and renewal of the Holy Spirit. The two are connected here. In fact, in some of the oldest Baptismal rites, an exorcism was part of the ceremony (Lutherans kept this using the words, “depart, you unclean spirit, and make room for the Holy Spirit in the name of the Father and of the Son and of the Holy Spirit”). We can inductively conclude that Baptism also delivers the Holy Spirit. The last thing that needs to be said about this passage is to explain what “regeneration” is. Regeneration comes from the greek word “palingenesia” (from “palin“, meaning again and “genesis” meaning birth… among other things). It literally means “new birth” or to be “born again”. So, to be a “born again Christian” means nothing other than being baptized.
It is my hope that this somewhat “brief” study has been helpful. While I do not claim to have exhausted what Scripture says about Baptism, these passages should shed light on the various descriptive events where people are Baptized (namely in the book of Acts). As a Christian, for me Baptism is part of my identity. This is why I say “I am Baptized” rather than “I was Baptized.” I love and cherish this gift and I hope every Christian can value this gift as I do because when it is all said and done, it places us right in Christ.