Robust boundary-localised modes and band geometry arise in a variety of condensed matter lattice systems, of which the Haldane honeycomb model is a paradigmatic example. We study a non-Hermitian variant of the Haldane model, which exhibits two key features: distinctive exceptional point (EP) structures in the periodic and open boundary spectra and non-chiral edge modes. In a fully periodic system, there are exceptional rings (ERs) that mark the boundary between the PT-unbroken and PT -broken regions, revealing Berry-curvature confinement across the PT -symmetry transition. The system on a cylinder with zigzag boundaries exhibits a bifurcation transition of edge-to-bulk delocalisation. We also observe a “Russian-doll-like” cascading of exceptional points as the non-Hermiticity is increased and we demonstrate how this is inherited from the bulk ER structure. The non-chiral edge modes remain robust against disorder in the non-Hermitian hopping parameter. The dynamical evolution shows a tunable range of weak non-Hermiticity and wave packet widths for which the edge-to-bulk delocalization time is extended. Therefore, the aspects of this model provide a natural platform to explore Berry-curvature confinement, exceptional-point cascading and non-chiral edge physics.