Do our bodies still technically exist when we die?

Unless they've been vaporized in a nuclear blast, yes.  But so do our immortal spirits, otherwise God would have to create new and innocent lives to unfairly reward or punish for what we did.  We ourselves would not care, having ceased to exist.

Our imperfect physical bodies decompose and become part of the earth. But we will be given perfect glorified bodies of a different nature, which we cannot fully comprehend at this time.

If you are a believer in Jesus Christ, you will one day receive a glorified body that will never wear out or die. The truth is that death leads to heaven or hell, and the only way to heaven is through faith in Jesus Christ.

The Bible is very clear that no one can earn their way to heaven since good works do not pay for sins. See Gal. 2:16, Rom. 3:23-28, 4:4-5, Eph. 2:8-9, Tit. 3:5. The only way to heaven is by believing in Jesus for His free gift of eternal life. Jesus shed His blood on the cross as the full payment for our sins. He did all the work; all He requires of us is that we believe in Him. Once you believe in Jesus Christ to save you, you are secure forever!

Because we have all sinned against a perfectly holy and righteous God, we all deserve eternal separation from God in hell (Rom. 6:23). However, God loves us so much that He sent His only Son Jesus to die on the cross as our Substitute so we don't have to go to hell. Christ died for our sins, was buried, and rose from the grave three days later (1 Cor. 15:3-4). He gives eternal life freely to anyone who simply believes in Him for it. No one can be saved by doing good works. Salvation is by grace alone through faith alone in Christ alone (Eph. 2:8-9).

"Verily, verily, I say unto you, He that believeth on me hath everlasting life" (John 6:47).

Matthew 25:46 

And these (the wicked) shall go away into everlasting punishment: but the righteous into life eternal.

No, the body is just a physical and transient shell for the spirit which is eternal.

The spirit is unseen but of perfect form for in God there is no imperfection. 

He gives the spirit and we do to that whatever we do and then the rewards are given out ...

or not.

The atoms exist.  

Are people named Jennifer?  Anonymous people never seem to know the answer to that question.

Sort of.  The faithful will receive a resurrection body, Philippians 3:20-21, 1 Cor. 15.

They will revert back to their basic mineral components.

Yes, for a while. Not forever.

Your body is only a vessel for your soul. Your body is essentially your automobile for life itself. That’s always how I thought of it.