Death and Hades just means the realm of the dead get thrown into the lake of fire to experience a second, permanent death.
"But the cowardly, the unbelieving, the vile, the murderers, the sexually immoral, those who practice magic arts, the idolaters and all liars—they will be consigned to the fiery lake of burning sulfur. This is the second death.” - Revelation 21:8
Would contradict what you're trying to imply. "That because death died there is no more death"... Yes... Because there's no one left to die since they've experienced the final, permanent death... Lol.
You're essentially trying to say "because they died the second death, and now there's no more death because all of the dead are dead, that means the dead must have eternal life because they can't die anymore!" Lol
Wrong!
We have already seen that the antichrist and false prophet exist in the lake of fire for 1,000 years and still alive.
We see these who take the mark suffer for eternity and have no rest . No matter how others try to reinterpret this- people live in th elake of fire.
Death and the grave experience death? How do inanimate things die? no they are destroyed in the lake of fire before those tossed in go just as Scripture shows.
Jesus vanquishes death at the end of time before eternity is "established" and time ends. The righteous already have immortality.
24 Then cometh the end, when he shall have delivered up the kingdom to God, even the Father; when he shall have put down all rule and all authority and power.
25 For he must reign, till he hath put all enemies under his feet.
26 The last enemy that shall be destroyed is death.
27 For he hath put all things under his feet. But when he saith all things are put under him, it is manifest that he is excepted, which did put all things under him.
28 And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him, that God may be all in all.
If all the unrighteous cease to exist- then Jesus does not conquer death!
But like the rich man suffering in the place of torments, the unrighteous shall suffer forever in the lake of fire that was designed just for teh devil and the rebellious angels.