Is it OK to re-write an article with the same information, just worded differently?

Facts themselves are not copyright. Everything about how they're presented is.

If you "re-write" and article and publish or redistribute it, it can be copyright infringement, and likely fraud.

You can reuse the facts. But you need to do more than "reword" the article. And you ideally should be confirming the facts with multiple sources. You have problems if you use just one.

No. Don't plagiarize.

Yes. This is often what my teachers would tell me to do.

No

no