Four reactions NH(a(1)Delta) + H'(S-2) are investigated by the quantum mechanical real wavepacket method, taking into account nonadiabatic Renner-Teller (RT) and rovibronic Coriolis couplings between the involved states. We consider depletion (d) to N(D-2) + H-2(X-1 Sigma(+)(g)), exchange (e) to NH'(a(1)Delta) H(S-2), quenching (q) to NH(X-3 Sigma(-)) + H'(S-2), and exchange-quenching (eq) to NH'(X-3 Sigma(-)) + H(S-2). We extend our RT theory to a general AB +C collision using a geometry-dependent but very simple and empirical RT matrix element. Reaction probabilities, cross sections, and rate constants are presented, and RT results are compared with Born-Oppenheimer (BO), experimental, and semiclassical data. The nonadiabatic couplings open two new channels, (q) and (eq), and increase the (d) and (e) reactivity with respect to the BO one, when NH(a(1)Delta) is rotationally excited. In this case, the quantum cross sections are larger than the semiclassical ones at low collision energies. The calculated rate constants at 300 K are k(d) = 3.06, k(e) = 3.32, k(q) = 1.44, and k(eq) = 1.70 in 10(-11) cm(3) s(-1) compared with the measured values k(d) = (3.2 +/- 1.7), k(q + eq) = (1.7 +/-0.3), and k(total) = (4.8 +/- 1.7). The theoretical depletion rate is thus in good agreement with the experimental value, but the quenching and total rates are overestimated, because the present RT couplings are too large. This discrepancy is probably due to our simple and empirical RT matrix element.