Questions:

1.  Will people die during the millenial reign of Jesus?
2.  Why, during such a wonderful time and Satan bound, will so many turn against Jesus?
3.  Will His rule of law be the Torah?

Answer:
From what I read in scripture, the curse of death will be suspended and man will live out his full day as Adam originally should have. I believe this to be the general rule. I believe we are given a clue in Isaiah 65:20 ,as I speculate that this is speaking of that period.

Isaiah 65:20

Amplified Bible (AMP)

20 There shall no more be in it an infant who lives but a few days, or an old man who dies prematurely; for the child shall die a hundred years old, and the sinner who dies when only a hundred years old shall be [thought only a child, cut off because he is] accursed.

I think we can be dogmatic in saying that any unnatural death will be an aberration and very rare. We know that there will be no death through violence and demonic activity for Satan is bound and Christ rules with a rod of iron through His supernatural, resurrected saints over the cities of the world. Of course, at the very end of this period, after the thousand years, things change drastically, as the Devil is loosed from his prison and goes about to deceive the nations again. God then sends a final rain of judgment down on all the wicked and the final judgment proceeds and evil is completely done away with, as He creates a new heavens and a new earth. Only the resurrected righteous will inhabit this new world, as the wicked had been previously judged and thrown into the Lake of Fire with Satan and all his minions. (Revelation 20)

2. Why, during such a wonderful time and Satan bound, will so many turn against Jesus?

Contrary to popular belief, all the wicked on the earth will not be destroyed at Jesus’ second coming (Armageddon). A remnant of humanity will be left alive on the earth, very much like we espy in our science-fiction movies. The difference being, Christ will be ruling and will restore, rehabilitate and replenish the earth. Yet, except for the resurrected saints, these will be unregenerate men living under a righteous dictatorship of the Eternal Son of Man but not regenerated in their spirits. They will still possess the sin nature yet, in a suppressed state due to  lack of the  demonic influence and temptation and the beautiful and equitable environment Christ establishes. This is why, when Satan is loosed they are so easily deceived and emboldened to try to overthrow Christ in Jerusalem. (Revelation 20)

3. Will His rule of law be the Torah?

According to the Old Testament and Intertestamental prophets and prophecies this appears to be the case for the unregenerate population, as the Law of Moses is the perfect moral and civil Law of God to keep evil in check and society under discipline and wise guidance. This will not apply to the resurrected saints who are no longer possessed of the sin nature and will continue to operate under the Law of Liberty, as brought forth in New Testament teaching for the Church which is, the Law of Love.