correct and guide

  1. May I take some of your food, please?
  2. Can I have some eating of your food?
  3. Can I have a bite?
    Are these sentences OK?
    Is there any other methods of asking the same query?
    Please correct and guide.

1 is grammatically correct, but sounds as if you wish to walk away with it!
May I share… would be better.

2 is incorrect. You could say
Can I have some of your food to eat?

3 is okay in informal situations.