"What do you want?" "Come, and you will see." (John 1:37-39)

Here Jesus is responding to two of John the Baptist’s disciples, who said:
"Rabbi, where are you staying?" (John 1:38).
Why were the disciples of John so interested in Jesus all of a sudden? It is because John the Baptist - their spiritual teacher - told his two students:
“Look, the Lamb of God!” (John 1:36)
What does this statement mean: "Lamb of God"? What is a “lamb” of someone else? A lamb is a subservient animal - one who defers to the herder. This is, in other words, an analogy. 'Lamb of God' is describing one who is humbly devoted to the Supreme Being.

This is not how many people like to translate the word lamb. They like to think of lamb as an animal that gets slaughtered, because they themselves slaughter lambs and eat them. However, we know that John the Baptist did not eat lamb:
His food was locusts and wild honey. (Matt. 3:4)
This means John the Baptist was a vegetarian. "Locusts" - from the Greek word ἀκρίς (akris) - does not refer to the insect, but rather, to the pods of the locust tree - which contain the carob bean. (They were called 'locusts' because the shape of the pods resembled the appearance of the locust insect - giving rise to the term, "locust tree.")

We also know from descriptions of Jesus, that Jesus did not eat red meat. Thus we can understand that when Jesus' teacher, John the Baptist, referred to Jesus as the "lamb of God" he was not referring to Jesus being slaughtered. John was referring to Jesus as being someone who was devoted to the Supreme Being.

Jesus also referred to himself this way later:
"For I have come down from heaven not to do my will but to do the will of Him who sent me." (John 6:38)
In other words, a lamb of God would be someone who was completely subservient to God, and willing to sacrifice everything on behalf of God. So describing Jesus as the "lamb of God" meant to describe Jesus as the humble, loving servant of God, who had given his life to the Supreme Being.

The day before, John also said:
"Look, the Lamb of God, who takes away the sin of the world!” (John 1:29)
Was this referring to Jesus’ dying on the cross for our sins, as many among ecclesiastical sectarian institutions have proclaimed?

What is "sin"? According to scripture, sin is acting in a way that goes against the will of the Supreme Being. Consider what God's will is, as taught by Moses and Jesus:
“ ‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment. And the second is like it: ‘Love your neighbor as yourself.’ All the Law and the Prophets hang on these two commandments.” (Matt. 22:37-40)
Sinning is the opposite consciousness of loving the Supreme Being - sinning requires a self-centered consciousness. Sinning is acting in a way that is not pleasing to the Supreme Being. Since what is pleasing to God is to love Him and love others, then acting selfishly - in love of our self - means to sin.

Some have twisted Jesus' instruction to "Love your neighbor as yourself." to mean we must love ourselves first before we can love others. 

This is preposterous, because if we are loving ourselves, we cannot follow the initial instruction, to "‘Love the Lord your God with all your heart and with all your soul and with all your mind.' " 

Yes - the phrases, "with all your heart" and "with all your soul" and "with all your mind" necessarily negate loving oneself first. They quite certainly mean loving the Supreme Being first.

The question is, if God was truly all-powerful, why would He need to make His servant suffer on a cross to remove people's sins?

God can remove sins of anyone simply by willing it, which is why Jesus taught his students to ask God for forgiveness for their sins in the Lord's Prayer:
He said to them, "When you pray, say:" 'Father, hallowed be Your Name, Your kingdom come.Give us each day our daily bread.Forgive us our sins, for we also forgive everyone who sins against us." (Luke 11:2-4)
Why did Jesus teach his students to ask God (Father) for forgiveness if all they had to do is wait for his crucifixion?

The fact is, this notion of the murder of Jesus' physical body being some sort of sacrifice for our sins so that we can go on sinning and wiping our sins off on Jesus is a hoax. It is a teaching created by sectarian teachers to gain followers by making purification cheap and easy - without requiring a change of heart. Jesus made a clear statement about such teachings along with those who teach them:
"Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but only the one who does the will of my Father who is in heaven. Many will say to me on that day, 'Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?' Then I will tell them plainly, 'I never knew you. Away from me, you evildoers!'" (Luke 7:21-23)
Rather, the manner in which Jesus can take away sins is accomplished by his teachings and his example. By teaching us to love and serve God, and by showing us how to love and serve God ("does the will of my Father") Jesus could effectively remove the sins of those who followed him. How so? By changing their hearts. By convincing them to give their lives to the Supreme Being.

This is how our sinful nature is purified. Sins are not removed by some magic trick. It is not a passive act. The Supreme Being does not remove the consequences of self-centered activity on a whim. The consequences of self-centered activities are part of the Supreme Being's system of learning within the physical world. Without consequences, we would continue our self-centeredness with no hope of having a change of heart.

But should we begin to learn the lessons borne of consequences, and approach the Supreme Being humbly, asking for forgiveness, the Supreme Being forgives our past sinful nature. This is Jesus' teaching, as evidenced by Jesus' request to turn to God and pray to Him:
"Forgive us our sins, for we also forgive everyone who sins against us." (Luke 11:4)