1. James is **doing** judo on the playground with his friends and he’s very excited.  
   **B. doing**

2. Keep **studying** Jessica.  
   **C. studying**

3. My father's **having** a cup of coffee with his colleagues in the living room now.  
   **D. having**

4. William always **has** breakfast with bread, eggs, and milk before coming to school.  
   **C. does** (However, "has" would be the most appropriate verb here, but it's not listed as an option.)

5. Tiffany and Rosy usually help their mom **do** the chores at the weekend.  
   **B. do**

6. She usually **studies** English vocabulary every morning.  
   **D. study** (However, "studies" would be the correct form, but it is not listed as an option.)

In summary, the best answers considering grammatical accuracy are:
1. B
2. C
3. D
4. C
5. B
6. D (but should be "studies" instead)