During synchronized waves oscillation (alpha beta etc...) do neurons fire only once for each wave cycle? Or can they fire few times then pause and again, firefew times and pause periodically? 
If  the second case happens then do we know if the neurons that fire in synchronity fire the same number of times at 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.