During synchronized waves oscillation (alpha beta etc...) do neurons fire only once for each wave cycle?
Probably, the "oscillation" refers to the signals of eeg/ecog/meg? If this is the case, then the answer is NO, individual neurons in a local network are firing with much higher rate then the frequency of the oscillatory field produced by the network. (Otherwise, the oscillations would look more like a ripples, not like the periodic function.) The exact number of spikes of any given individual neuron is vary over time within a certain range and most probably different from one cycle of the network-level oscillation to another. 

In general, individual neuronal activity is probabilistic, not deterministic. So, any natural situation is changing the probability of the spike, but it is never 100% predictable.