2 is not OK. that does a double duty as a relative conjunction word and a relative pronoun.
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StephenLaiSo, the sentence"that I do is right" is grammatically correct.
But, what really confuse me is what exact does this sentence mean.
It isn't quite grammatically right.
I think you need an object there:
That I do it is right.
which means:
That fact that I do it is right.
(as Incho's menti