Pearsons product Moment correlation coefficient and Chi- square test can do in testing the significance unless the sample size is low t-test may not be convenient here
My guess is that the Wilcoxon rank-sum test would be adequate for testing differences between the two groups. The number of intervals in your scales is important and I assume that you have around 5. For 1) I would run this test for each variable, adjusting for the four comparisons by setting the critical p-value to 0.0125 (if you are happy with a family-wise Type I error rate of 0.05). For 2) the product-moment correlation would be adequate, as already suggested, but again an adjustment for the multiple comparisons is recommended. For 3), you might try two nonparametric linear models, one for each response variable. It is necessary to justify why you have chosen the particular relationships that you are testing, or reviewers may suspect that you have just tested all possible relationships and only reported some.
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