Enhancements of residual Reynolds stresses and symmetry breaking with resonant magnetic perturbations (RMPs) are presented. These experiments were performed using a Langmuir probe array in the edge plasmas of the J-TEXT tokamak. This study aims to explain the mechanisms for generating residual stresses and intrinsic rotations. It is observed that with RMPs, peaked residual stresses, steeper pressure gradients and stronger shear layers all appear around the resonant surface. The toroidal rotation is accelerated in the direction of the plasma current and shows a correlation with turbulence and the measured residual stresses near the resonant surfaces of RMPs. Symmetry breaking induced by magnetic islands is proposed as a new mechanism, which qualitatively explains the enhanced residual stresses and the acceleration of the toroidal rotation. The changes to the residual stresses and symmetry breaking with RMPs near the last closed surface are also discussed.