I Must Work the Works of Him

Who "sent" (John 9:4) Jesus?
God the Father.

Until when did Jesus "work" on earth "the works of" (John 9:4) God the Father?
Until the "day" ended and the "night" (John 9:4) came - i.e., until the time set for His ministry on earth ended and He returned to heaven.

Why did Jesus say, "I am the light of the world" (John 9:5)?
He was reminding them of what He declared moments earlier, just before His heated exchange with the Pharisees: “I am the light of the world. He who follows Me will not walk in darkness, but will have the light of life” (John 8:12). He saw a blind man who had been living in literal "darkness" (John 8:12), had compassion on him, and was going to put His words into action by lighting up the blind man's world both visually and spiritually.

When does the day end and the night come for Christians?
When we die and go to heaven.

What are we supposed to do until then?
Be Jesus' light to the world: “You are the light of the world. A city set on a hill cannot be hidden. Nor do they light a lamp and put it under a basket, but on a lampstand, and it gives light to all those in the house. Let your light thus shine before men, that they may see your good works and glorify your Father in heaven" (Matthew 5:14-16).

Have you been His light to the world or just to your church?
 

Doesn't being His light to the world invite danger and persecution?
Jesus stopped to help the blind man while distancing Himself from a mob that was trying to stone Him to death (see Before Abraham was I AM), and told us that we will be persecuted as well: see John 15:18-19 in You did not choose Me, but I chose you and John 15:20 in If they persecuted Me, they will persecute you.