I'd like to perform Pearson correlation analysis on a data set. To my understanding the Pearson correlation test requires the data to be normally distributed. My questions regarding these are the follows:

1. Let's say, I have 100 observations, and 3 dimensions. The normal distribution should be tested dimension by dimension? I mean I pick the first dimension, and test, whether the 100 data in that dimension are normally distributed? Then I do it the two remaining dimensions, correct?

2. If my point 1 is correct, then what if all the data are normally distributed in each dimensions, except one, or more?

3. Could you give me a method/procedure (preferably in open source statistical package R) how to best test the normal distribution of data?

4. If the normal distribution fails, what other correlation test is applicable what is not based on ranking (like Spearman and Kendal tests)?

Thank you for your help!