Here are the correct boxes ticked for countable and uncountable nouns:

1. A lot of children like playing video games. (Countable nouns) ✔
2. There is not much sugar in the bowl. (Uncountable nouns) ✔
3. Would you like another burger? (Countable nouns) ✔
4. In the mountain, it's very cold in the winter. (Countable nouns) ✔
5. Help yourself to some more rice. (Uncountable nouns) ✔
6. Remember to close the window when you leave. (Countable nouns) ✔
7. Mary drinks orange juice for breakfast every day. (Uncountable nouns) ✔
8. The visitors arrived with a lot of luggage. (Uncountable nouns) ✔
9. Don't eat too much food before you go to bed. (Uncountable nouns) ✔
10. We need to buy some toothpaste. (Uncountable nouns) ✔