Should I remove features such as gender and birth month before drawing the heatmap because they are categorical?

I am working on a dataset that has both categorical and numerical (continuous and discrete) features (26 columns, 30244 rows). Target is categorical (1, 2, 3) and I am performing EDA on this dataset.

• The categorical features with numerical values (ex: gender has values 0 and 1) are also considered when taking the heatmap with seaborn. As per my knowledge, the heatmap is drawn to check the correlation between continuous numerical features right (correct me if I am wrong). Should I remove such features before taking the heatmap?
• I have another feature named born month. Is this also a categorical feature as it can only take values from 1-12? If so, I need to remove this one also before drawing the heatmap right?
• Should I do a test like the Chi-Square test on those features?