This paper proposes and experimentally validates a joint control and scheduling framework for a grid-forming converter-interfaced Battery Energy Storage Systems (BESSs) providing multiple services to the electrical grid. The framework is designed to dispatch the operation of a distribution feeder hosting heterogeneous prosumers according to a dispatch plan and to provide frequency containment reserve and voltage control as additional services. The framework consists of three phases. In the day-ahead scheduling phase, a robust optimization problem is solved to compute the optimal dispatch plan and frequency droop coefficient, accounting for the uncertainty of the aggregated prosumption. In the intra-day phase, a model predictive control algorithm is used to compute the power set-point for the BESS to achieve the tracking of the dispatch plan. Finally, in a real-time stage, the power set-point originated by the dispatch tracking is converted into a feasible frequency set-point for the grid forming converter by means of a convex optimization problem accounting for the capability curve of the power converter. The proposed framework is experimentally validated by using a grid-scale 720 kVA/560 kWh BESS connected to a 20 kV distribution feeder in the EPFL campus hosting stochastic prosumption and PV generation.