I think you need to get some professional help. Everyone feels like this to some degree and certainly the thought of losing people we love, the futility of life and other painful concepts along these lines don't ever get easier to deal with, but if they're threatening to take over your life then it's quite different. If you have suffered/are suffering from depression, these feelings are probably an extension of your illness and you may find that therapy and perhaps some anti-depressants help.
In terms of good, common sense advice the thing I tell everyone (which my mother in turn told me) is to bear in mind that life will always find ways to surprise you with horrible events - it's never the things you worry about that happen, it's always stuff you would never, ever expect. I don't say that to worry you more but to make you realise that just because you have a fear of something happening, doesn't mean it will happen. When I look back on the awful things that I have seen or that have happened to me in my short life, I realise I never could have seen any of them coming. I would never have devoted any time pondering the possibility of them occurring or worrying that they would happen because they were just the unlikeliest things. And the things that I would lie awake crying about never happened. So when I consider it like that, it makes me wonder why I ever bother worrying about things at all!
Worrying about how you will feel when the inevitable happens, e.g. when your parents die, is another issue, because obviously it will happen at some point. I guess all I can say is that worrying isn't going to make it happen at a different time - when it does happen yes it will be awful but you can't change that. It's something absolutely everybody goes through at some point in their life and you just have to deal with it. Hopefully by the time you get to a point where it's becoming a realistic concern, you will have your own family to focus on. Losing your parents at an age where you are still very much dependent on them must be incredibly difficult - losing them when you are an adult with your own life is still dreadful emotionally but it's not the same in terms of the upset in your life balance.
Anyway I seem to have written a lot about very little. I guess my point is worrying is natural but not to the point where it's becoming an impediment to living your life normally. Get some counselling to help you deal with it and maybe tell your parents too - perhaps you just need to let them know how much they mean to you, and I'm sure they'd be incredibly glad to hear you say it.