Am I crazy? If I am, would I realize it?
Why can't I use will here? I think it is in first conditional form. So will should be used
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If you were to substitute will here, you would change the meaning of your question to involve the future. Your question becomes one of determining the fact at some unknown future time.
A more standard way of phrasing in the present tense would be either
Am I crazy? If I were, would I realize it?
or more colloquially
Am I crazy? If I were, how would I know?
Note the use of were which in this case is about conditionality, not about past tense.
First, you are expressing a hypothetical, so you should use the conditional form "would" instead of "will".
Second, you have an error previously in your second sentence by using the word "am" in "If I am", it should be if I were, this is called the subjunctive mood, which is used when expressing a non factual conditional.