I am struggling to find out a suitable way to calculate correlation coefficient for categorical variables. Pearson's coefficient is not supported for categorical features. I want to find out features with most highest influence on the target variable. My objectives are:

1. Correlation between categorical and categorical variables. e.g. For a binary target (like Titanic dataset), I want to find out what is the influence of a category on the target (like, influence of gender on survival (0/1))
2. Capture some non linear dependencies. e.g. For supermarket sales data, the sales is usually higher during weekends as people might visit such store more during holidays. So we expect to see spikes at an interval of roughly 7 days. Is there any way to capture this non-linearity/seasonality by a correlation coefficient?