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We consider a two-lead (three-terminal) setup of nonlocal transport through Majorana zero modes (MZMs) and construct a Majorana master equation (which is also valid for small bias voltage). We first carry out representative results of current and then show that a modified Bogoliubov-de Gennes (BdG) treatment can consistently recover the same results. Based on the interplay of the two approaches, we reveal the existence of nonvanishing channels of teleportation and crossed Andreev reflections even at the limit $ε_M\to 0$ (zero coupling energy of the MZMs), which leads to new predictions for the height of the zero-bias-peak of the local conductance and the $ε_M$-scaling behavior of the teleportation conductance, for verification by experiments.