Just wanted to clear some misconceptions I have about regression analysis. Your help would be highly appreciated

1) One of the assumptions for a regression analysis is the normal distribution of residuals at every value of the predictor value.

This does not mean that ALL the predictor values have to be standardized for regression analysis, right? It just means that I should check via P-P plot that the residuals for each variable are normally distributed - am I right?

I got confused by the following information:

"Regression assumes that variables have normal distributions. Non-normally distributed variables (highly skewed or kurtotic variables, or variables with substantial outliers) can distort relationships and significance tests. There are several pieces of information that are useful to the researcher in testing this assumption: visual inspection of data plots, skew, kurtosis, and P-P plots give researchers information about normality, and Kolmogorov-Smirnov tests provide inferential statistics on normality. Outliers can be identified either through visual inspection of histograms or frequency distributions, or by converting data to z-scores. " - http://pareonline.net/getvn.asp?n=2&v=8

2) Am I right in assuming that conducting regression analysis (normal moderation analysis) on PROCESS should yield the same results than conducting a regression analysis on SPSS without the PROCESS plugin?

Thank you!