Are the structural model (Merton), the reduced form model and the binomial method all credit risk models? I am not quite sure about the hierarchical structure between arbitrage-free models, credit models, structural model, reduced form and binomial model.

The structural and the reduced form model are both credit risk models. Risk neutrality is the assumption in both of these models (as in most financial models). My understanding is that the the binomial tree is just a method used in both models to arrive at a solution. You can use the binomial tree to calculate any option prices, not just credit risk models.