I recently read a paper where the authors used either (a) a generalised linear model or (b) a combination of Wilcoxon rank sum tests and Spearman’s rank correlation, depending on whether the data followed a normal distribution or not. They also used a Bonferroni correction when applicable, to account for multiple comparisons.

The responses were two continuous variables, each analysed separately. They had 3 categorical variables and 1 continuous variable as independent variables. 
(a) For the first response variable, data followed a normal distribution, so a GLM was fitted assuming a normal distribution with identity link. Inference was (apparently) made by significance of model terms, i.e. whether or not the independent variable was significant in the model or not. 
(b) For the second response variable, the data did not follow a normal distribution, so a Wilcoxon rank sum tests and a Spearman’s rank correlation test were used instead.

My questions are:

1) Are these two approaches appropriate and equally valid alternatives, depending on (non)normality?

2) Even in case of non-normality, wouldn't a different GLM type be better than a combination of Wilcoxon rank sum tests and a Spearman’s rank correlation? (Not sure which type of GLM would be appropriate though, as the response is still continuous...gamma perhaps?)

3) In a GLM framework, aren't we worried about non-normality of residuals, rather than raw data (which is not always the same thing)? 

4) Doesn't a GLM (**generalized** linear model) with "normal distribution and identity link" simply mean a **general** linear model (i.e. an ordinary linear model)?

5) Is this approach of using p-values from a full model (including all variables) appropriate, or would a variable selection (using AIC or similar) be more appropriate?