The first normal stress difference (N1) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in dilute granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behavior in the dense limit. As in the elastic hard-sphere fluids, N1 remains positive (if the stress is defined in the compressive sense) for dilute and moderately dense flows, but becomes negative above a critical density, depending on the restitution coefficient. This sign-reversal of N1 occurs due to the microstructural reorganization of the particles, which can be correlated with a preferred value of the average collision angle θav=π/4±π/2 in the direction opposing the shear. We also report on the shear-induced crystal-formation, signaling the onset of fluid-solid coexistence in dense granular fluids. Different approaches to take into account the normal stress differences are discussed in the framework of the relaxation-type rheological models.