Answer to Question 1
The Wilcoxon rank sum test compares two independent samples, while the Wilcoxon signed rank test can be used to compare two dependent samples. The Wilcoxon rank sum test should be used with independent samples, and the signed rank test should be used when dealing with pairs.
Answer to Question 2
The parametric counterpart to the Wilcoxon signed rank test for paired samples is the paired samples t-test. Both tests assume continuous data on the interval or ratio scale, and the data come in pairs. The t-test assumes that both underlying populations are normally distributed, whereas the Wilcoxon test assumes only that both distributions are fairly symmetric in shape.
