1. I go to academy for my English.

Question

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'?]

Answer 1

2, 3, 5, 7, and 8 are fine. The others aren’t.

Yes, you need those articles in these sentences.

Answer 2

Yes, you need to use "a" or "the" when the academy is a common noun, not the name of the school. If the name of the school was English Academy, "a" or "the" would not be necessary since it is specific. So, you go to "a" private institute, "an" academy, etc. I"n number seven, do you own the academy, making it yours? "My" academy indicates possession, like your car or your shirt. Number one seems awkward. It should be "the" or "an" academy, and "my" English is not a phrase that seems comfortable. "to learn" or "to study" English would be much better.