Did Jesus take the punishment for everyone's sins on the cross? Is 1 John 2:2 relevant to this?
1John 2:2 And he is the propitiation for our sins: and not for ours only, but also for [the sins of] the whole world.
Yes, but it will not profit anyone who is not willing to forsake all and follow Him. As Jesus said, 'you must be born again'.
John 3
3:1 There was a man of the Pharisees, named Nicodemus, a ruler of the Jews:
3:2 The same came to Jesus by night, and said unto him, Rabbi, we know that thou art a teacher come from God: for no man can do these miracles that thou doest, except God be with him.
3:3 Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God.
3:4 Nicodemus saith unto him, How can a man be born when he is old? can he enter the second time into his mother's womb, and be born?
3:5 Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and [of] the Spirit, he cannot enter into the kingdom of God.
3:6 That which is born of the flesh is flesh; and that which is born of the Spirit is spirit.
3:7 Marvel not that I said unto thee, Ye must be born again.
3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
3:17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
3:19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
3:20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved.
3:21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.