IMO it's just about making it age appropriate, but also about explaining the reasons why we don't worry about certain things. For example with hurricanes you could explain that hurricanes are a thing that only happen in certain areas of the world because different parts of the world have different climates which means they get different types of weather. That's why it rains very much in England but Australia is usually sunny and hot, Lapland usually has snow all winter, etc. You could explain that Florida is a particular part of America where the climate means that hurricanes can happen, but that hurricanes are very rare in Britain and when we have had hurricanes, they are not anywhere near on the same scale and normally just mean very strong winds, nothing like houses being blown away.
You could also explain that houses in America are often made of wood which means that they tend to blow away more easily than British houses which are usually made of bricks, stone or concrete. (Wooden houses can be more stable in earthquakes).
Also accepting the feelings - it's okay to be sad and worried about people in America right now because they are in a frightening and dangerous situation, that's a proportionate response. I know it can be our instinct to want to make it all better but actually you can't always make things better. It can help DC to develop skills of empathy if you let them have the sad feelings and acknowledge that it is a terrible thing for people.
But I do admit - DS was about 5 when that passenger plane was shot down a few years ago and I exclaimed oh my god they've shot down a plane, and he asked me "Did the people have to go down the emergency slide?" and I hesitated for about a second and lied "Yes, I expect they did." In that case it was because we live abroad from family and I did not want him to suddenly develop a fear of flying, and I was finding the news upsetting and difficult to process myself, but normally we'll talk about things openly.
Recently (he's 8 now) he heard about the Grenfell Tower fire and was alarmed about the fact it started in a fridge. So we were able to talk about how although that was a very shocking and frightening event, actually the circumstances of that particular fire were highly unusual and don't apply to the block that we live in. And also that the family with the fridge fire actually were some of the first people to escape because they knew about the fire so early. It actually gave us a good reason to talk about what you should do if you ever find yourself in a fire which was a good reminder, and he seemed to feel better after that once he knew what he should do.