Recently, stationary plasma with a world-record pulse length of 1056 s was achieved on the Experimental Advanced Superconducting Tokamak (EAST). In this work, the core magnetohydrodynamics (MHD) events as well as mode coupling processes have been investigated in EAST long pulse operation with electron heating dominant and pure radio frequency wave heating low collisionality, by using several diagnostics and the nonlinear numerical code M3D together. A saturated m/n = 1/1 kink mode was observed in the core region, where a stable internal transport barrier was found in the electron temperature channel. The frequencies and 2D structures of these modes were studied by a combination of soft X-ray (SXR) imaging and electron cyclotron emission diagnostics. The frequency of the m/n = 1/1 mode exhibited a feature of chirping down with time, and this chirping rate corresponds to the rate of electron diamagnetic drift frequency change. A twisted pattern ('Taichi structure in shape') was reconstructed by SXR tomography of the m/n = 1/1 mode. The perturbations of electron temperature and density caused by m/n = 1/1 are different in size, the latter one being much smaller. The destabilization of m/n = 1/1 was due to the strong central heating combined with electron cyclotron resonance heating and lower hybrid current drive. In the presence of the m/n = 1/1 mode, a negative current was generated on the magnetic axis, which anomalously broadened the core current profile. A m/n = 3/2 tearing mode triggered by m/n = 1/1 mode was also observed. The m/n = 3/2 mode has a smaller frequency than the m/n = 1/1 mode, and carries an m/n = 3/2 island with detectable size. A novel 3D MHD model that separately evolves the plasma density and temperature is applied to the m/n = 3/2 triggered by m/n = 1/1. It is found that a toroidal current density at the q = 1.5 surface, caused by non-axisymmetric density perturbation during the m/n = 1/1 nonlinear growth phase, was generated and hence the destabilization of the m/n = 3/2 tearing mode. Both the modeled electron temperature and density perturbations agree well with experimental observations. In the last section of this paper, the interaction between the m/n = 1/1 mode and fast electrons as well as the active control of this mode are also presented.