1. If we don't go to school, we go to academies.

2. If we don't go to school, we go to an academy.
3. If we don't go to school, we go to academy.
4. If I don't go to school, I go to academies.
5. If I don't go to school, I go to an academy.
6. If I don't go to school, I go to academy.
[Which sentences are ungrammatical? Would you check articles and plural forms at the end of each sentence?]

1 is fine

2 is fine
3 - no. If there is only one academy, we need to say "the academy". If there are more than one, we need to say "an academy." Only if the academy's proper name is Academy may we omit the article.
4 - no. Do you (singular) go to several academies, more than one?
5 - is fine
6 - see #3 comment above.

Let's analyze each sentence to determine if they are grammatically correct and if the articles and plural forms are used correctly:

1. If we don't go to school, we go to academies.
- This sentence is grammatically correct. The plural form "academies" is used correctly.

2. If we don't go to school, we go to an academy.
- This sentence is grammatically correct. The singular form "an academy" is used correctly.

3. If we don't go to school, we go to academy.
- This sentence is grammatically incorrect. It should be "we go to an academy." The singular countable noun "academy" requires an article before it.

4. If I don't go to school, I go to academies.
- This sentence is grammatically correct. The plural form "academies" is used correctly.

5. If I don't go to school, I go to an academy.
- This sentence is grammatically correct. The singular form "an academy" is used correctly.

6. If I don't go to school, I go to academy.
- This sentence is grammatically incorrect. It should be "I go to an academy." The singular countable noun "academy" requires an article before it.

So, the ungrammatical sentences are 3 and 6. Both of them lack the necessary article "an" before the singular noun "academy."