1. Why does God command all his angels to worship his Son?
and having been found in appearance as a man, he humbled Himself, having become obedient to death—even death of a cross Phil 2:8-11
Therefore God also highly exalted him, and granted to him the name above every name
that at the name of Jesus every knee should bow, in the heavens and on earth and under the earth,
and every tongue confess that Jesus Christ is Lord, to the glory of God the Father.
Some say Jesus is God. If that were true,
- the Son would not be exalted beyond what he already was - how can one be higher than being God ?!
- how could he die as God is immortal?
- how can he be become obedient - does God have subordination issues within Himself?
God isn't commanding anyone here. He is inviting celebration and recognising the joyous accomplishment of defeating evil on just terms as He parades His firstborn and heir amongst the heavenly beings - with the devil no doubt looking on!
God...in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom He also made the ages. 3 And He is the radiance of His glory and the representation of His nature Heb 1:2
(It seems odd that if Jesus is God, he is representing God's nature. He is representing God precisely because he cannot be God!)
No one before or after has accomplished what Jesus did. Adam #1 began without sin but crumbled under pressure of temptation.
Jesus, Adam #2, also a man, also began without sin, but through suffering, became obedient to death. How was this done - because he was God?
No, he succeeded in victory over evil not by fraud or trickery! As if God could be tempted or tricked by the devil. As if God could sin and die as Jesus could. As if God needed to learn obedience.
During the days of Jesus’ earthly life, He offered up prayers and petitions with loud cries and tears to the One who could save Him from death, and He was heard because of His reverence. Heb 5:7
This is Jesus seeking the assistance from his Father and God to help him stay the course and not succumb to temptation, not let his will (which sometimes differed from the Father) take precedence.
This has nothing to do with his death on the cross - a death Jesus did die and that victoriously. Did God save him from that death? No. It was for that death that he came!
Now My soul has been troubled, and what shall I say? 'Father, save Me from this hour'? But on account of this I came to this hour. John 12:27
2. What is it about his Son that makes him worthy of worship by all God's angels without provoking God to jealousy?
This is a silly question. Why would God call to worship His son and then get jealous about it?
3. What does this tell us about his Son's nature?
This doesn't tell us anything about the son's nature - except that he isn't God! What else would God's angels be doing except worshipping God? When the son takes up his new spot at God's right hand, they can worship him too - I'm sure God is loving having His amazing son by His side at last - forevermore!
There are plenty of other verses that do inform about Jesus' nature precisely and consistently. There is no need to make up stuff about Jesus that the bible has forgotten to include - or has become outdated and needing the wisdom of men to sort out.
Just a note about the 'firstborn' inclusion. Heb 1:6
Jesus is not firstborn before Adam. Jesus was born ~4BC to Mary. Get the whole story here as explained in Colossians.