How to avoid duplicate content on my own site?

That has nothing to do with duplicate content: that's syndicated content. The differences between the two are briefly explained in this post and this little article.

And how and why do you imagine so many lower page-rank pages are outranking so many higher page-rank pages all over Google's SERP's every day of the week, then? Or weren't you aware of that little detail (even in spite of its having been explained to you so many times before, here?).

By the way "sites" don't even have page-ranks, though their home pages and other pages do: only pages have page-ranks.

Google doesn't "penalize" sites for duplicate content at all (unless it determines that the duplicate content is a deliberate and flagrant attempt to deceive their algorithms, but that clearly has nothing at all to do with the issue being discussed in this thread).

Just a suggestion for you: it's better to have a look at things like Google's WebMaster Central Blog for yourself than it is to repeat all this stuff based on Google having some fictional "duplicate content penalty", because what you're saying here is exactly the way that these urban myths of internet marketing are perpetuated and propagated.

Probably because your site is newish? If it's that, then it's probably temporary, and will rectify itself as long as you continue gradually to acquire initial indexations of articles subsequently syndicated elsewhere. Or it could be because it's not-so-newish but has incurred the wrath of Google over some of your previous backlinking efforts. There's certainly a lot of that about, because people do like buying backlinks and seem quite oblivious to the damage it can do them.

Thanks for all your input in this discussion!!

Isaan