1. He's very busy.

2. He is very busy.

3. He's never been to New York.
4. He has never been to New York.

5. He's sad yesterday.
6. He was sad yesterday.

7. They were happy.
8. They're happy.
9. They are happy.

10. They're scared yesterday.
11. They were scared yesterday.
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Is #5 wrong?
Does #8 mean #9? What about #7?
Does #10 mean #11?

These contractions are correct as long as they're in present tense.

5 and 10 are incorrect.
8 is correct only if it means the same thing as 9.