Yes.
God says humans are mortal. When Joshua was very old and about to die, he said he was about to go the way of all the earth. Because dying is what everyone on earth does. Solomon says all come from dust and all return to dust, because death is the destiny of everyone. People are destined to die. Isaiah says all people are like grass that withers.
The Bible says all people are subject to death, because all people have sinned. No matter how rich you might be, no payment can ever be enough to redeem your life so that you can live forever. Isaiah suggests that even in the afterlife, people will still die. It will just take longer before they do.
Zephaniah says not only is everyone mortal, but one day everyone is going to die at the same time and leave no one alive! God is going to sweep away everything from the face of the earth, destroying all mankind. The whole earth will be consumed with fire, and God will make a sudden end of all who live on the earth.
No.
David is immortal. God chose him to be king over Israel forever.1 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.
The gospel of John claims that whoever believes in Jesus will not perish, but will instead have eternal life. It has Jesus state that anyone can eat him and not die. And that whoever obeys him will never see death. And that he has given his followers eternal life, and they’ll never perish. And that whoever lives by believing in him will never die.
The book of Hebrews claims that God took Enoch to heaven alive, and he never experienced death. And that Melchizedek’s life had no end.
Paul says when the world ends, some people will still be alive. They’ll get caught up in the clouds to live with God forever. It doesn’t sound like those people are going to die. Paul also claims that Jesus has destroyed death. If that’s true, then no one has died for the last 2000 years! And no one will ever die in the future, either.