Does everything we eat have carcinogens?

No. If we did eat food with carcinogens in them we would be dead at an early age. Always check labels on whatever you eat.

In trace amounts. The air you breathe also has trace amount of carcinogen. You can reduce your risk of cancer by adopting healthy habits: Eat a mostly vegetarian diet, avoid alcohol, tobacco and street drugs, avoid excessive exposure to sun, get HPV vaccine, exercise 30 minutes each day, drink enough water so your urine is mostly colorless.