1. He is happy as well.

2. He is not happy as well.

3. He likes apples also.
4. He doesn't like apples also.
5. He also doesn't like apples.

6. He didn't sing, too.
7. He didn't sing, either.
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Can we use 'as well', 'also', and 'too' in negative sentences?
Can we put 'also' at the end of a sentence? Which ones are not grammatical?

1, 2, 3, 5, 7 are all fine.

For 4, I'd just leave our the "also."
For 6, I'd use "either" instead of "too."

Of course, it might be different if I could read these sentences in the context of a conversation or a story, not as single sentences.