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The MMPI calculates scale scores from dichotomous responses; hence those scale scores – the constructs of actual interpretive interest – are roughly continuous, or at least polytomous.
Yes, there are very many other tests that can assess personality traits that can aid in diagnosis. I'm not sure what you mean by "mature", and I hesitate to judge their sophistication.
I'm guessing by "INFJ" you're referring to the Myers–Briggs Type Indicator, of which "INFJ" is one available type. Typology is one primary difference from the MMPI, which measures traits in terms of continuous dimensions. I'll leave the rest of the differences to Wikipedia for now.