I'm really having a hard time trying to normalize my data. My study is about green IT product acceptance. There are eight factors, six are 5-point Likert scale (Str.disagree - Str.agree), one is 2-point Yes/No question, and the other one is 3-point scale (Don't know/Maybe/Know). I have 618 returned questionnaires.

I add data into SPSS, compute variables, and round them up. I explored skewness and kurtosis of all factors and found that they're not normally distributed. I tried a Two-Step Transformation to Normality and Box-Cox, but the KS and SW Sig. are still .000. However, Q-Q plot change from loosely distributed to perfectly follows the slope.

My questions are:

1. Is it a crucial problem if my data isn't normally distributed?
2. Someone said Likert scales are not normal in their nature, is that true?
3. Do you know any literature to cite and explain why Likert scale isn't normally distributed?
4. Do I need to normalize all variables before I do Structural Equation Modeling?