Accumulating evidence relates the fine-tuning of synaptic maturation and regulation of neural network activity to several key factors, including GABAA signaling and a lateral spread length between neighboring neurons (i.e., local connectivity). Furthermore, a number of studies consider short-term synaptic plasticity (STP) as an essential element in the instant modification of synaptic efficacy in the neuronal network and in modulating responses to sustained ranges of external Poisson input frequency (IF). Nevertheless, evaluating the firing activity in response to the dynamical interaction between STP (triggered by ranges of IF) and these key parameters in vitro remains elusive. Therefore, we designed a spiking neural network (SNN) model in which we incorporated the following parameters: local density of arbor essences and a lateral spread length between neighboring neurons. We also created several network scenarios based on these key parameters. Then, we implemented two classes of STP: (1) short-term synaptic depression (STD) and (2) short-term synaptic facilitation (STF). Each class has two differential forms based on the parametric value of its synaptic time constant (either for depressing or facilitating synapses). Lastly, we compared the neural firing responses before and after the treatment with STP. We found that dynamical synapses (STP) have a critical differential role on evaluating and modulating the firing rate activity in each network scenario. Moreover, we investigated the impact of changing the balance between excitation (E) and inhibition (I) on stabilizing this firing activity.