In a cell-free wireless network, distributed access points (APs) jointly serve all user equipments (UEs) within the their coverage area by using the same time/frequency resources. In this paper, we develop a novel downlink cell-free multiple-input multiple-output (MIMO) millimeter wave (mmWave) network architecture that enables all APs and UEs to dynamically self-partition into a set of independent cell-free subnetworks in a time-slot basis. For this, we propose several network partitioning algorithms based on deep reinforcement learning (DRL). Furthermore, to mitigate interference between different cell-free subnetworks, we develop a novel hybrid analog beamsteering-digital beamforming model that zero-forces interference among cell-free subnetworks and at the same time maximizes the instantaneous sum-rate of all UEs within each subnetwork. Specifically, the hybrid beamforming model is implemented by using a novel mixed DRL-convex optimization method in which analog beamsteering between APs and UEs is conducted based on DRL while digital beamforming is modeled and solved as a convex optimization problem. The DRL models for network clustering and hybrid beamsteering are combined into a single hierarchical DRL design that enables exchange of DRL agents' experiences during both network training and operation. We also benchmark the performance of DRL models for clustering and beamsteering in terms of network performance, convergence rate, and computational complexity.