My parents are really old and I'm worried about them?

My parents had me quite late. My dad is 68, my mom is 50 and I'm only 13. A lot of times, people confuse me as their granddaughter. I'm also kind of worried about people making fun of me in high school because my parents are so much older than theirs'. And I'm not ashamed of my parents at all, I love them to pieces. But my mom has lung and kidney cancer and I'm really worried about her dying soon as well as my dad since he's really old. Just the past week my mom told me we're going to go look at grave plots for them! Which terrified me all the more! I think my dad is in good health (he's still working and does a lot of tough jobs around the house) but he's also got arthritis and my mom is always in pain because of her chemotherapy, so they're not as energetic when we go places. Ahh...I'm just really worried and scared for them, because I don't want them gone before I even get married or have kids...