Hey, I'm sorry to hear you've been going through such a rough time. Life certainly can put us to the test sometimes, and it can be hard to learn how to deal with all of it.
I want to share a quote with you from a favorite author of mine, that has really helped me when I'm overwhelmed or down.
People are like stained-glass windows. They sparkle and shine when the sun is out, but when the darkness sets in, their true beauty is revealed only if there is a light from within. 
Life isn't always going to be sunny and perfect, unfortunately. Oftentimes we are faced with adversity, and that is that time in life when we can either chose to stand up to it, or to just step back and let it overcome us. You say that your life is slowly falling apart, and that you can't fix it; but I refuse to believe that you aren't the type of person who chooses to fight through adversity. From everything I've seen of you, you seem like you've got quite a bit of spunk in you, and I do believe that you can put up a fight and get through this.
You say that you were diagnosed with something that could kill you. The key word here is "could". This is the 21st century, and the medical advances we have made are phenomenal. Listen to your doctors, and take care of yourself. Do everything you possibly can to help the healing process. The human body has the ability to overcome a lot. All you have to do is help it along. Additionally, if you need someone to talk to about whatever is going on here, definitely feel free to send me a PM. If you give me a little more information about what's going on medically, perhaps I can offer you a bit more support and advice here.
I'm sorry to hear about your grandpa. The death of a loved one is certainly hard to deal with. One thing that really helped me to cope was to go back and try to think of all the good moments I had with that person. At first, it's sad thinking of it and knowing that the person is no longer around, but sooner or later you start to realize that those memories will always be alive in your memory, even after the person has passed. Remember that your grandpa probably would rather have you think back about him and be happy about how much he loved you, rather than be sad that he's gone. I know this is easier said than done, but in time I think it's something that you can come to terms with.
In regards to your parents, I believe there are several choices that you have about how to deal with all of this. The first, and best choice (if it's a possibility) would be to try to communicate with your mom and dad. I'm not sure what the grounds were for you mother kicking you out, but I feel that oftentimes things like this are the result of a long period of time with poor communication. Maybe there was a fight, or maybe something was done that really hurt one of you. In either case, I think that if you can you should really try to talk to your mom. This may involve taking the higher road and accepting part of the blame for the falling out. If you really express to her that you want to have a good relationship with her, and that it's really important to you to have her in your life, maybe she will be willing to try to heal your relationship.
Communication can also help with your father. Have you ever brought it up to him that you would like to have more of his support? Again, try telling him how important having him in your life is. Be honest with him and tell him that you really do need him right now, more than ever.
However, I know that sometimes communicating with people isn't the ultimate solution to your problems. Sometimes, unfortunately, people just aren't willing to listen. I have a good idea of what you're going through right now; I have no contact with either of my parents whatsoever, and have basically been told that I'm not to return home again. I've tried talking to them but sometimes things get to the point where the best solution is time. If this is the case for you, allow yourself and your mom a chance to get your lives back together. Let the steam blow off, and allow each other time to put the past in the past. Time has a tendency to heal wounds, and hopefully once you've both had some time to yourselves, you can come back later and sort out your differences.
In any case, try not to let your family's issues drag you down too far. I understand that family is a big part of everyone's life, but at the same time, you need to be able to step back from that. You've got a future and plenty of potential and the ability to rise above this. I know it's not easy, but always remember that at the end of the day, the only person who can truly hold you back is yourself. Anything else can be overcome, if you fight for it.
Again, I know that you're going through a rough time but I do have faith that you can get through this. You've got it inside you; you just need to allow yourself to rise above instead of letting other people's setback drag you down. Use these upcoming exams as a way to do this. Study hard, and allow your thoughts to be on something else for a while. If your focus is on doing well on the exams, it will be harder to dwell on the negatives.
Finally, remember that there is always someone to turn to. If no one else, turn to me. I would be happy to listen or help you out any time you need it. Send me a message anytime.
Remember, keep fighting and stay strong. You can pull through this.
Take care.
-Isobel