This paper investigates a cell-free multiple-input multiple-output integrated sensing and communications (ISAC) system, focusing on channel estimation and coordinated beamforming while minimizing system overhead. To achieve this, we jointly optimize pilot sequences during channel estimation and coordinated beamforming during data transmission to enable more efficient target detection. Specifically, at the central processing unit, we employ a Transformer for channel estimation and a graph neural network (GNN) for coordinated beamforming. First, we propose a time-division duplexing protocol for channel estimation and coarse target detection. A supervised learning approach is adopted to approximate the optimal solution, leveraging a well-trained dataset. Second, we model the cell-free ISAC network topology as a heterogeneous graph, comprising different types of nodes and edges, and employ a GNN-based approach for coordinated beamforming. Both learning models are trained offline and deployed online. Simulation results demonstrate the effectiveness of the proposed schemes in terms of channel estimation accuracy, target detection performance, and quality of communication signals.