1. I go to academy for my English.
2. I go to an academy to learn English.
3. I go to an English academy after school.
4. I go to English academy to learn English.
5. I go to a private institute to learn three subjects such as English, math and science.
6. I go to private institute every day to learn three subects.
7. I go to my academy five times a week.
8. I went to the academy after dinner.
[Which expressions are grammatical? Do we need to use 'a' or 'the'?]
1. I go to an academy for my English. [grammatical; use of "an" suggests that there are multiple academies, and this person goes to one of them for their English studies]
2. I go to an academy to learn English. [grammatical; use of "an" suggests that there are multiple academies, and this person goes to one of them to learn English]
3. I go to an English academy after school. [grammatical; "an" is used because "English academy" is treated as a specific type of academy]
4. I go to an English academy to learn English. [grammatical; "an" is used because "English academy" is treated as a specific type of academy]
5. I go to a private institute to learn three subjects such as English, math, and science. [grammatical; "a" is used because "private institute" is not treated as a specific institute]
6. I go to a private institute every day to learn three subjects. [grammatical; "a" is used because "private institute" is not treated as a specific institute]
7. I go to my academy five times a week. [grammatical; "my" suggests that the speaker has a specific academy in mind]
8. I went to the academy after dinner. [grammatical; "the" is used because it refers to a specific academy, possibly mentioned earlier in the context]
2, 3, 5, 7, and 8 are fine. The others aren’t.
Yes, you need those articles in these sentences.