Reply to "verb tenses"

Now that I know (a) "It was surprising that he should have committed the crime" is correct, I wonder WHY? Why can't we simply say "It was surprising that he committed the crime"? What are the differences between the following sentences?

1. It was surprising that he should have committed the crime.
2. It was surprising that he committed the crime.
3. It was surprising that he had committed the crime.

4. It is surprising that he should commit the crime.
5. It is surprising that he commits the crime.
6. It is surprising that he has committed the crime.

By the way, I suppose we can use either of the following to describe things happened in the past. Am I right?

- It was surprising that he should commit the crime.
EQUALS
- It was surprising that he should have committed the crime.

Lastly, would it be ungrammatical to say "It is surprising that he committed the crime"?

Thank you very much in advance! Smile
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