Properties of the Chi-Square Goodness-of-Fit Test

Consider the following statements regarding the chi-square goodness-of-fit test.

I. For a categorical variable with 5 categories, the degrees of freedom for the test are $5 - 1 = 4$.

II. A necessary condition for the test is that all expected counts must be at least $5$.

III. The test uses the $t$-distribution to determine critical values.

Which of the statements is/are true?