How to do backward features elimination when considering interactions between them
My first question is : for example, if the highest p value is for the X1X2 feature, is it okay to eliminate this feature even when X1 and X2 can be statistically significant ?


  Of course, the interaction can have no information about the target. Per example if the problem is perfectly defined by X1 and X2. The interaction $X_1 \cdot X_2$ won't add nothing to the model.


My second question : in the case when all the interaction of some feature have a p value greater than 0.05 in the first iteration, Could I eliminate this feature and all the interactions ?


  I would try a more experimental approach of removing them only if they don't improve the model accuracy rather than having a low P-Value. 


As a further reccomendation I would reccomend sklearn.