What must I do to be saved? What does the Bible say about salvation?
Welcome to these forums dear brother in Christ. I hope that in a spirit of Christian Love and humility you will be open to hearing the responses to your comment offered in this forum. I am glad you quoted some scripture here but I believe you missed quite a few others. I believe we should not pick and choose and accept ALL that is given to us for our Salvation.
Here’s a brief summary of what I see when I read about salvation in the scriptures:

Love the Lord your God with all your heart, soul strength and mind and Love your neighbor as yourself. Luke10:25-28

Repent of your sins and…Acts2:38

Baptize with water and the Spirit. Mark16:16, John3:3-5, Tit3:5, 1Pet3:20-21, Acts2:38

Believe and Accept the Gospel: the good news of our Lord Jesus Christ. Rom1:16, 1Cor15:1-4 Acts16:30-31

Confess my sins James5:16, 1John1:19, John20:19-23

Do the will of the Father. Matt5:19-20, Matt10:38, Matt16:24-25, Mark8:34, Luke9:23, Luke14:27, Phil1:29 +

Eat the flesh and Drink the blood of Our Lord Jesus Christ. John 6:51-58 1Cor10:16-17, 11:23-30, Apoc19:9, Luke14:15, Isaias25:6-9

LOVE of Neighbor. Luke10:33, Matt25:31-46, Acts26:20, Hebrews13:15-16

Live in Holiness. Hebrews12:14

Accept the cross(suffering and trials) Matt10:38,16:24-25, Mark8:34, Luke9:23, Luke14:27, Phil1:29+

Persevere and Stand firm to the end working for your Salvation with fear and trembling. Matt10:28, Matt24:13, Mark13:13, Phil2:13

Childbearing + faith+ love+ holiness in sobriety. Tim2:15

Be perfect as your heavenly father is perfect. Matt5:48

Saved through Gods Grace by our Faith in Christ which is confirmed by Works. James2:24, Ephesians 2:8-10, Romans 3:24, 1Thes 5:9, John 3:36, Acts 15:11

He who LOOKS to the Son and believes in Him shall have eternal life (John 6:40) our Lord says this when He is proclaiming His True Presence in the Eucharist. He is asking us to gaze upon Him and Believe that He truly is present in the bread and wine of the Lords Supper (the lambs supper/the mass).

Love the Truth 2Tes 2:10
If you read all these scripture passages you will find that there’s is quite a bit of “doing” for us Christians to do. This is because “faith by itself, if it does not have works, is dead.”(James2:17)
We MUST BE READY AND STAY DRESSED FOR ACTION for the master will come unexpectedly. The servant(christian) who knew His master’s will and DID NOT DO IT will get a “severe beating” Luke12:36-47. Note that here Our Lord is talking about those of His household (Christians). Those who do not know His will (non-Christians) and did not do it will receive a “light beating”(Luke12:48) The more we receive the more will be asked of us. As Christians we will be judged more severly because much has been entrusted to us. As a Catholic I will face an even stricter Judgement because I’ve been exposed to the FULLNESS OF THE CHRISTIAN FAITH and much will be required of me (Luke 12:48). As Saint Paul said “Woe to me if I don’t preach the gospel” and he continues to say “I discipline my body and keep it under control, lest after preaching to others, I myself will be Disqualified.” (1Cor 9:16,27) Even such a great man of God as saint Paul was, he did not dare to boast a guaranteed assurance of salvation as many today claim to have without yet having faced judgement.
As I read all these opportunities for Salvation I recognize our great God’s goodness, His Immense Love and Awesome mercy! I know and Recognize that Our Lord Jesus Christ is the door for Salvation (John 10:9) and offers us many opportunities for our salvation but even those who “believe they are saved” will face Judgement (2Cor 5:10) and many who think or “believe” they’ll make it in will not enter the kingdom of God and many whom we may think will not enter the Kingdom of God will inherit Eternal Life. The door is narrow, many are invited but few will enter. Few will Hear the voice of our Lord say “Well done, good and faithfull servant…enter into the Joy of your master.”(Matt 25:23) “Who then will enter the kingdom of God?” We believe in our Lords awesome Love and Mercy and we hope for the Salvation of ALL for this is God’s own will (1Tim 2:4) and we also believe that many who do not live up to these expectations of our Lord will be saved but as those who pass through the fire of purification (1Cor 3:15) because nothing unclean will enter the Kingdom of God (Rev 21:27)
John 6:47: (Jesus) Verily, verily, I say unto you, He that believeth on me hath everlasting life.
Brother you did quote John 6 to confirm that we must “believe” but it seems you’re missing the whole point of our Lord’s message here and what specifically he is asking his followers to believe about Him here. In John 6 our Lord repeats himself like he does no where else in scripture. He must have had an important point: He really wants you to “believe” that He is the “Bread of Life” and that you should “believe” and do the “work” of eating Him.
John 10:28: (Jesus) And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand.
Now, you all agree that God cannot lie, right?
And if He says that He will give eternal life to anyone who believes in His son, wouldn’t that be true? But if He then would take that eternal life away, it didn’t last forever, did it? And He lied…
Which He can’t.
My Friend let us keep in mind who Our Lord is talking about here. If you read verse before In John 10:27 you will notice that our Lord is talking about the sheep that “hear his voice” and “follow him” and whom He KNOWS. This promise is for those who seem to be doing some stuff: hearing, following and who are recognized by Him. As you quoted in Matthew 7:21-23, it is those who “do the will of the Father” that are recognized and known by Him.