Explain Orthogonalization and Cross-Fitting in Double ML

A subscription company wants the effect of a price discount on 12-month retention. Discounts in the last year were not randomized: account managers gave them mainly to customers with high usage and high contract value. The data scientist proposes LinearDML in EconML with gradient boosting as nuisance models and 5-fold cross-fitting. The head of analytics asks you to justify every part.

1. Explain, with the Frisch-Waugh-Lovell (FWL) idea, what is being residualized and what the final regression looks like.
2. What does "orthogonal" buy you, concretely, when the nuisance models are flexible and imperfect?
3. Describe cross-fitting step by step and state the problem it prevents. What would you tell someone who says "it is just a data-splitting ritual"?
4. What assumptions does DML not remove, and which checks would you run before trusting the estimate? Would you use DML if the discount were randomized?