Yes.
The Bible says God alone is immortal. Humans can’t live forever, because they didn’t eat from the tree of life, because God didn’t want them to. He made us mortal, limiting our lifespans, because he didn’t want to have to deal with us forever. And since God never changes his mind and nothing he does can ever be changed, we will definitely always be mortal.
Everyone sins, so everyone has to die. No one can redeem anyone’s life and convince God to let them live forever. No one can even choose the time of their own death. Death happens to everyone on earth, no matter how wealthy or wise they are. Death is the destiny of everyone. All people return to dust, like withering grass.
One day God will wipe out all mankind from the earth. Then after God creates a new and better world, where people live longer, even then people will still die. And people who have died never come back to life, either. Dead people stay dead forever.
No.
God isn’t the only one who’s immortal. He made angels immortal too. There are also immortal worms in hell. As for humans, why would God tell people to rejoice forever if he knew they weren’t going to be able to do that, because they weren’t even going to live forever?
David is immortal. God chose him1 to be king over Israel forever. God gave David everlasting life, because he asked for it. David will trust God forever, because God will never abandon him to the realm of the dead and let him decay. Instead, God will let David live in his house forever, where he will praise God forever, because he will be happy forever.
Some of the other psalmists must be immortal too, since they’re going to obey God and praise God forever. Enoch never died. And Melchizedek’s life not only has no end, but no beginning either.2
God has chosen some people to be given eternal life. That has always been his intention. On Mount Zion, God gives people the gift of everlasting life and everlasting joy. Jesus gives people bread and water and fruit from the tree of life (as well as more unusual things to eat and drink) that give them eternal life. People who consistently do good will live forever. So will people who please God. Everyone who believes in Jesus or believes what God says will be given everlasting life. People who obey God and Jesus never die.
Anyone who keeps God’s commandments, sells everything they have and gives to the poor, and follows Jesus will be given eternal life. So will everyone who hates their life. So will anyone who abandons their family because they think Jesus wants them to. So will God’s slaves and servants. So will people who have so much worldly wealth that everyone wants to be friends with them. So will people who make a “good confession” to many witnesses, whatever that means. And some people will get eternal life not because of anything they did, but because somebody else worked for it.
The Bible says one day death will be abolished, which means everyone will be immortal. Or at least everyone who hasn’t already died by that time. But can all those dead people really stay dead permanently if no one is cast off by the Lord forever? No, he’s going to have to resurrect everyone who ever lived and let them live forever.
Then after people are resurrected with imperishable bodies, and mortals become immortal and move to their eternal home in heaven, they will be like angels, unable to die. Even people who go to hell will still live forever, so they can be tormented forever, along with the devil, the beast, and the false prophet.
Wait, actually death won’t even need to be abolished, because Jesus already destroyed death thousands of years ago. God gave people imperishable bodies way back then. We’re all immortal already!