I think the media's influence will be positive in some cases and negative in some cases. It really depends on the type of disaster, location, and other factors. As I think of Hurricane Katrina, the media outright perpetuated negative stereotypes and partcipated in biased reporting. Just an example, they called the evacuees (who are United States citizens) 'refugees.' A lot of the media bias had to due with the fact that many of the victims were Black and extremely poor.

Some of your questions are too specific to speak of in general terms.  There are some cases where the certain media corporations or networks have hurt victims with intrusive reporting, however even in these cases we cannot lump all media together.  Some media networks are out to get the big stories, all the attention, and sensationalize any disaster.  Other media networks follow more traditionally ethical journalism practices. 

Media has certainly changed the way we view disasters.  It has even changed the way we talk about them.  For instance, hurricanes are now given names rather than numbers.  Hurricane Ida will get far more attention than hurricane number 593.  Sometimes this shift is attention is a good thing.  We reach out and help others that we might not have even known about.  We feel more connected to the outside world.  Look at the number of US programs in place to help Hatti after the disaster there.  Other times this shift is not a good thing.  Victims of a disaster can be overwhelmed. 

I know I personally lived in a neighborhood that was hit by a large tornado.  The media attracted a lot of attention.  While some of this attention was good (people offering assistance and aide), a lot of it was bad.  The police had to come and guard the area because so many people were trying to get in and have a look.  It was difficult to get to our house and pick up the pieces because we had to get past on lookers and later security.

The media does have one unintended effect on disasters.  While the spotlight is on, there is awareness and help pours in.  Yet once the spotlight is off, the help dries up.  This is the unintended consequence of media attention.  All of that attention and money also leads to increased greed and corruption sometimes.  We saw this in Haiti, for example.  Long after the TV cameras are gone, the problem remains.  Few are in it for the long haul.

While the media are certainly motivated by their desire for a story, and the coverage of disasters often smacks of exploitation, it is also true that by raising awareness of disasters, they pave the way for more assistance, both by encouraging aid and by raising political pressure on the government to intervene to help. In some cases media coverage can help hold politicians and government agencies accountable for their failings in responding. This was true of Hurricane Katrina. On a slightly unrelated note, it is also true that expansive media coverage of the weather saves lives. Being able to follow tornadoes in real time gives people warnings far quicker than before, allowing them to get to safety. The Weather Channel and other outlets also do a good job in educating people as to how storms work.

At least in tangible terms, the media helps the victims of disasters.  For example, if the Indian Ocean tsunami of 2004 had happened in 1904 (or probably even 1954) before the time of the internet and cable TV news there would not have been as much in the way of private donations being made to help the victims because people would not have felt the impact of that event so much.

In terms of disasters, I really don't believe the media has an agenda, they are just looking for a story.  I think its biggest concern is to present a compelling story that will grab the attention of its audience, and sensationalist coverage is a big part of that.  I guess one positive to this is that when the media does grab the attention of its audience, people tend to donate or volunteer to help the survivors of the disaster.  So they do play a role in helping bring attention to the disaster.

The modern media has undoubtedly increased the awareness of disasters in all parts of the world. In many cases, this awareness has resulted in increased aid and humanitarian response.

Of course, the media can also be manipulated by skillfull politicians for their own benefit. It can draw funding to an afflicted area which is then stolen. It can be used to accuse authorities of conspiratorial acts of terror for the political gain of someone else (see Hurricane Katrina).

Like everything else, it can be a tool for good or evil, depending on how it's used and who is using it.