The sociologist doesn’t make any claims about whether most (over half) newspaper stories are about violent crime. She states only that there are many newspaper stories about violent crime.

The sociologist's conclusion is that there aren't a lot of violent crimes. One premise supporting this conclusion is that violent crimes are very rare. But "violent crimes are very rare" is the conclusion stated in different words. The sociologist is using the conclusion as its own support, which makes the argument circular. If you don't already accept the conclusion that violent crimes are rare, the premise gives you no independent reason to start believing it.

The sociologist's argument doesn't depend on newspaper stories being unbiased. The sociologist is only concerned with why newspapers print so many stories about violent crimes, not with whether those stories are fair or accurate in how they cover the crimes. Whether or not the coverage is biased has no bearing on the sociologist's reasoning, so this isn't something the argument needs to assume.

A part-to-whole flaw would involve assuming that what's true of individual members of a group must be true of the group as a whole. The sociologist's argument doesn't involve reasoning from properties of individual crimes to properties of crime overall, or anything similar. The flaw here is about circular reasoning, not about confusing parts and wholes.

The sociologist's argument is entirely about the current state of violent crime. There's no comparison between what has happened in the past and what will happen in the future. The argument is about what's true right now.