Violation of regression conditions-HELP!!

For my thesis, i need to analyse association between 1 DV and several IV (which are either binary, ordinal and continuous). My DV scores from 0 to 27. My data are quite skewed. I have 402 observations in total. I tried to run regression analysis. However the assumptions for regression analysis are:
1. Residuals should be normally distributed
2. Residuals should have a constant variance
3. Independence of errors.

While I comply to the third condition, I am not meeting the first 2. Here are the graphs for the residuals. I have removed the outliers, but it did not change the normality heteroskedasticity of the residuals. Can anybody suggest me what I should do? Thanks