We don�t usually specify a time with the present perfect, so I would change the first one. Either remove "earlier" or change "Rachel�s been" to "Rachel went".
The second one is fine in the US, but I think British English would insist on using the present perfect, as Aisha suggested.
I would change the third one to "...on the test yesterday, but he didn�t cheat."
I agree with Aisha on the fourth one.
On the fifth one, say "The reporter is writing an article (or the article), but..."
Bruce