I thought it would be replaced by a New Heaven and Earth?
Just before God started creating, the amount of mass/energy in existence was zero.
Over a six-day period, the amount of mass/energy was raised to its current level.
At this point, God instituted the Law of Conservation (1st Law of Thermodynamics?) and rested (ceased from His work).
This means that God locked in the amount of mass/energy that was to exist forever and ever.
Because of the Fall, the universe is now "winding down" toward thermal equilibrium.
God is going to intervene before it reaches maximum entropy, separate all the atoms (with a great noise), then rearrange them into a New Heaven and a New Earth.
2 Peter 3:10 said:
But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
Someone might ask, "Why doesn't God just annihilate everything and start over?"
I believe that's because when He created the universe, He created it to last forever, and no amount of sin or science is going to intervene.
Why not Eve? She ate the fruit first, tempted Adam with it, etc.
By making Adam the federal head of the human race, God made Jesus Christ ("Second Adam") the Head of the Church.
Had He not done that, then Jesus Christ would have to come back and be crucified for each and every person that reaches the age of accountability.
Eve was tricked --- Adam wasn't.
When does one reach the 'age of accountability'? Or does it vary from person to person (like, say, puberty)?
It varies based on mentality and upbringing.
If someone's committed no sins by the time they've died, even after reaching the age of accountability, do they automatically enter Heaven?
No, they need cleansed of their Sin Nature.
As I said --- hypothetically --- if a person were never to have committed a sin, they would still go to Hell when they die.
Or do they have to be Christian (unlike babies)?
Let's put it this way --- they would have to be 'born again' (converted).
Does this 'age of accountability' have any Biblical basis?
Yes.
Matthew 18:3 said:
And said, Verily I say unto you, Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven.