Linear regression only requires normality of the regression residuals (error scores) in the population. Normality of the independent/predictor variables or the dependent variable is not required. So you could run your linear regression and check the distribution of the residuals. See, for example, Cohen, Cohen, West and Aiken's (2003) regression text.

Yes, linear regression only requires the normality of the regression residuals, the standard error term or "error scores". You can plot the qqplot assess the linearity. A good non-parametric equivalent to the Pearson Correlation is the Spearman Correlation (ρ), and is appropriate when at least one of the variables is measured (or can be ordered) on an ordinal scale. You can as well try Michael E. Sombre test. Here is a pre-print on non Parametric meditation test. https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.math.sciences.univ-nantes.fr/~philippe///Stat_%26_mediation_files/np_preprint.pdf&ved=2ahUKEwjaqPTrsM30AhUOjqQKHe2HClMQFnoECCcQAQ&usg=AOvVaw3sN30yWk_3hGDU8OOHgmcJ

Thank you, Christian Geiser and Abiodun Christian Ibiloye for your guidance. I did simple linear regression and Sobel test as suggested, and was able to complete my data analysis. Thank you once again!