Should we convert independent continous variables (features) to categorical variable before using decision tree like classifier?
There is no need to split continuous variables because the tree already does that automatically. The only way you can test for overfitting is by either using a holdout set or by doing cross validation. If you are overfitting, changing a continuous variable to a categorical variable likely won't make a difference. If you get the sense that you're overfitting, you should reduce the depth of your tree.