The further away a target goes, the harder it is to track. Both the US and Russia get around this by using satnav, Iran (to my knowledge) does not have this capability. Going across the border also means that Iran would have to deal with any sort of defenses that are there, it would also have to deal with potential detection of the missile, and deal with unknown terrain conditions (provided that the missile is hugging the ground to avoid detection, both visually and by radar, though radar isn't really an issue with Iraq).
The coverage only extends to what Iran is saying, nothing really more than that. I don't really buy that those other events were more important to the media to present over this, as this is a huge deal, if true.
This could very well be true.
Both American and Russia missiles, which you have to admit are more advanced, have shown system failures. I don't see why this particular missile couldn't fail either.
Maybe not leaks, but we could very well see an official complete video, or ground evidence from a third party. Iran has shown previously that it is willing to show evidence of its claims, for example, the video that showed Iran had successfully hacked the RQ170.
On the other hand, it is also unhealthy to simply believe someone, just because they're the primary source. A healthy amount of skepticism must always be exercised.