How to perform feature selection on dataset with categorical and numerical features?
It is fine to apply feature selection technique on one hot encoded variables. Because if one particular segment of that variable is correlated with your target, then it is a good news. Your model will understand the scenario better.
Or, You can label encode your categorical variable first so that you still have 30 variables (29 numerical + 1 label-encoded categorical variable). Now try to find the importance value of each variable, and take the relevant ones (Use any method for it: be it RFE, random forest feature selection, pearson's correlation etc). Once you have the final list of variables, and the label-encoded variable is also coming as relevant, it is ok to put it into the model.