This research delves into the aspects of communication and connectivity problems within random Wireless Sensor Networks (WSNs). It takes into account the distinctive role of the sink node, its placement, and application-specific requirements for effective communication while conserving valuable network resources. Through mathematical modeling, theoretical analysis, and simulation evaluations, we derive, compare, and contrast the probabilities of partial and full connectivity within a random WSN, factoring in network parameters and the maximum allowable hop distance/count hmax. hmax captures the diverse range of delay-sensitive requirements encountered in practical scenarios. Our research underscores the significant impact of the sink node and its placement on network connectivity and the sensor connection rate. The results exemplify a noteworthy decline in the sensor connection rate, dropping from 98.8% to 72.5%, upon relocating the sink node from the network center to the periphery. Moreover, as compared with full connectivity, partial connectivity and the sensor connection rate are more suitable metrics for assessing the communication capability of random WSNs. The results illustrate that 1.367 times energy is required to connect less than 4% of the remote sensors, based on the examined network settings. Additionally, to increase the sensor connection rate slightly from 96% to 100%, an additional 538% more energy is required in multipath fading based on the widely adopted energy consumption model. This research and its outcomes contribute to establishing appropriate performance metrics and determining critical network parameters for the practical design and implementation of real-world wireless sensor networks.