Which ML algorithm to use if we have categorical data, numeric data, derived data (derived from) other variable in our data set?
This question is way too vague, you just describes pretty much a standard situation. Which algorithm / method you use depends entirely on your objective and data. You should provide more information if you want a specific answer. Since your dependent variable is binary you are interested in classification, popular algorithms are Random Forests, Logistic Regression, K-means, etc.