Learn English – Is it right to say “While I was back on the way home”

You can use "Back in 2000" at the beginning of the sentence, at the end of the sentence, or any position inbetween.

Back in 2000, when Larry Smarr left his job as head of a celebrated supercomputer center in Illinois to start a new institute at the University of California, San Diego, and the University of California, Irvine, he rarely paid attention to his bathroom scale.

For yielding to the call of sticky goodness back in 2000, David's 11-year-old behind was bounced from his Douglas County elementary school.

I remember back in 2000, when Hillary Clinton first ran for the U.S. Senate, and this is what we found.

Could the state that gave us a murky verdict back in 2000 give us a clear winner this coming Tuesday?

Both your sentences are fine. As "for example" is a parenthetical, there should be a comma before and after it.

Back in 2000, for example, I built a robot.

Use "once I was back home" or "once I got back home.

1. Once vs when...

Once and when could both be used here generally speaking. However, using "once" here means that something is happening quickly after you arrive home. It's a little more dramatic and seems to match the tone of your story.

Using "when" also implies an order of events, but is a little more relaxed.

"Once" also makes it sound like it was a little more difficult to get back home.

2. Adding "I was" or "I got" to the sentence.

"When back home" is understandable in context, but "when I got back home" is clearer to the reader. It also proves to the reader that you did, in fact, go home. In some contexts, "when back home" could be read as "when I get back home". So the reader may think you are talking about the future instead of the present.