Answer:

Jesus "became sin for us" on the cross.  This is why Jesus cried, "My God, My God, why have you forsaken me.?"   God laid on him the sins of us all while on the cross.  2 Corinthians 2:14-21 describes this.  Also, Isaiah 53:5-7 tells us that God laid our iniquity on Jesus on the cross.

No, Jesus die not become sin for us when he was baptized.  No, he was not carrying our sin when he was tempted by Satan.  Jesus did NOT sin at this point.  He was sinless and remined sinless, until God imparted to him all of our sins on the cross.  This explains why Jesus was so upset in the Garden of Gethsemane.  It was not the physical pain that he was so upset about but the fact that he was going to receive the wrath of God on the cross (Matthew 26).

Jesus fulfilled all righteousness when he fulfilled all the requirements of the Law of Moses.  Jesus said that the law would not be removed or passed away, but that the requirements of the Law would be met by the first sinless man:  Jesus Christ.  I assume you are referring to Matthew 5:17. or perhaps to the baptism of Jesus by John.   Jesus did not just fulfill all righteousness, he brought in a new covenant of righteousness through his death on the cross.

Jesus completed the job of "fulfilling all righteousness" on the cross, but his entire life was the process of fulfilling all righteousness.

John Oakes