A possible solution is to train a prediction model for each dependent variable using all the dependentindependent variables in each case. Indeed, you can use different models in each case (in case you want to handle categorical and numerical data with different models).
Notice that since this approach treats each dependent variable independently, so possible relations between the predicted variables are not taken into account (if they exists).
Also check out scikit-multilearn package, but I have no experience using it.