Thank you for your help.

Question

3. He goes to the academy to take three subjects.
4. He goes to the specific academy to take three subjects. [specific]
5. He goes to the academy in general to take three subjects. [in generic use]
[What about #3? Does #3 mean #4 or #5?]

Answer 1

3 - OK

4 - I wouldn't use the word "specific" like this. I'd write this sentence like this:
He goes to the Adamston Academy to take French, guitar, and advanced math courses.

5 - I would not write this sentence this way; it's quite awkward. I'd write this:
He goes to an academy to take French, guitar, and advanced math courses.

Answer 2

I appreciate your help.

3. He goes to the academy to take three subjects.

[What about 'the academy' in #3? Does 'the acdemy' in generic use? Or does 'the academy' mean the academy which the speaker and hearer know already?]

Answer 3

Yes, your second version of #3 is fine.