I collected data on one sample, the DV could be separated into two groups (success yes vs. no) and then I have several IVs with interval scale. I just don't know if to use Wilcoxon or Man-Whitney test. Also I don't know if it's necessary to use Bonferroni correction or if that is just important for parametric tests.
The difference between the Mann-Whitney U and the Wilcoxon tests relates to the design of the >experiment. If your experiment has a repeated measures or matched participants design then >the Wilcoxon test is used to analyse your data. If your experiment has an independent >measures design then the Mann-Whitney U test is used to analyse your data.
IMHO @Giorgio's anwser is not correct since there are two Wilcoxon tests (namely, Wilcoxon Rank-Sum and Wilcoxon Signed Rank).
It might be useful to remember that Mann-Whitney test is also called Wilcoxon rank-sum test. And therefore, there is no difference in applying Mann-Whitney or Wilcoxon rank-sum tests. You should get the same result.
As I already wrote here, people do sometimes make a mistake in replacing Mann-Whitney with the Wilcoxon signed-rank test. The difference comes from the assumptions. In the Mann-Whitney test you are interested in the difference between two independent populations (null hypothesis: the same, alternative: there is a difference) while in the Wilcoxon signed-rank test you are interested in testing the same hypothesis but with paired/matched samples.
For example, the Wilcoxon signed-rank test would be used if you had replicates (repeated) measurements between different time points/plates/... since it is the same sample but measured in different time/on different plates.
As for the Bonferroni correction, the answer to this question highly depends on your setting. If you are going to torture your data until it confesses I would advise that you use a correction technique (like Bonferroni/FDR/Holm-Bonferroni/...) to protect yourself from false judgement. Regardless of the choice between parametric and non-parametric tests.