In surveying the rich reservoir of neuronal computations and brain functions, a natural question arises: what unified characteristics influence the diverse and heterogeneous dynamical states and computations in highly recurrent cortical networks? Seminal studies suggest that large-scale information processing results from interactions between the task environment, neuronal biophysics, and cortical architecture. While experimental advances have provided detailed cortical connectivity data, i.e. the connectome, it remains unclear which are fundamental for cognitive processing. Theoretically, Recurrent Network Networks (RNNs) can perform multiple tasks through dynamic states, but their biological relevance is limited by a lack of biological grounding. To bridge these gaps and obtain a unified view of cortical dynamics and cognitive computations, we integrate these findings by proposing a multi-area RNN (maRNN) with connectome-constrained inter-areal sparse connectivity, trained on 15 cognitive tasks. Locally, intra-areal dense connectivity is incorporated to further enhance the computational flexibility. After training, maRNNs concurrently exhibit highly random fluctuations within areas and structured communications between areas, enabling flexibility and coordination in multitask dynamics. Our analysis reveals that maRNNs exhibit distributed cross-areal task representations that are task-dependent. More than half of areas encode decision variables in simple tasks, while only higher areas, like those in the PFC, show substantial responses to decision variables in complex tasks. Additionally, we've identified information-gated computation along the areal pathway: primary sensory areas directly encode sensory stimuli regardless of their task relevance, whereas higher areas encode task-relevant information. Our results highlight the crucial role of connectome and macroscopic hierarchy in forming heterogeneous and dispersed neural representations in maRNNs. This model extends conventional task-oriented RNN studies for cognitive computations and introduces a novel approach to constrain RNN training with connectivity data, fostering a deeper understanding of multi-regional brain computations and communications.