Over-the-air federated learning (OTA-FL) integrates communication and model aggregation by exploiting the innate superposition property of wireless channels. The approach renders bandwidth efficient learning, but requires care in handling the wireless physical layer impairments. In this paper, federated edge learning is considered for a network that is heterogeneous with respect to client (edge node) data set distributions and individual client resources, under a general non-convex learning objective. We augment the wireless OTA-FL system with a Reconfigurable Intelligent Surface (RIS) to enable a propagation environment with improved learning performance in a realistic time varying physical layer. Our approach is a cross-layer perspective that jointly optimizes communication, computation and learning resources, in this general heterogeneous setting. We adapt the local computation steps and transmission power of the clients in conjunction with the RIS phase shifts. The resulting joint communication and learning algorithm, RIS-assisted Over-the-air Adaptive Resource Allocation for Federated learning (ROAR-Fed) is shown to be convergent in this general setting. Numerical results demonstrate the effectiveness of ROAR-Fed under heterogeneous (non i.i.d.) data and imperfect CSI, indicating the advantage of RIS assisted learning in this general set up.