I'm having huge issues with the assumptions of multiple regression and determining whether I am running my analysis correctly.

First of all, I have eight different predictors and one outcome variable. The idea is to determine whether each variable is a significant predictor of the outcome variable and their contributions to the overall regression model. Four of the variables are scale so no problems there. Two variables are dichotomous. However, the remaining two categorical variables have three levels.

I believe I am correct when I say that it is not possible to run a multiple regression with categorical variables with three levels. I have looked at videos with dummy coding variables but I am unsure whether it is possible to do so. In the case that I do go with dummy coding, is it possible to do dummy coding with other variables as predictors?

Also, my predictors with three levels are very disproportionate in terms of participant numbers. For instance, one variable had 36% of participants at level 1, 52% at level 2 and 12% at level 3. Is it still possible to include them as predictor in a multiple regression analysis despite the disproportionate numbers?