The post-sunset equatorial ionosphere is a scientifically intriguing region with implications for space weather and challenges for GNSS/GPS technologies. In this thesis, we carry out three separate research projects involving ultra-low-frequency waves and plasma density fluctuations using data from the Swarm satellite mission to enhance our understanding of this ionospheric region. In the first study, we explore interhemispheric magnetic field-line resonances (FLRs) during quiet times after sunset. We identified 26 FLRs, including one at the lowest reported magnetic latitude (2 degrees). Notably, in four instances, these waves were seen in both hemispheres during a Swarm pass, demonstrating that the waves extend along the entire field line. The fundamental frequency of these FLRs decreased as the field line length increased, in accordance with the theory. The second study centers on electromagnetic fluctuations within plasma bubbles. We observed strong coherency between electric and magnetic fields, reaching up to 5 Hz, with a phase shift of nearly 90◦. This observation along with changes in the Poynting vector sign within plasma bubbles are consistent with standing waves. The field-aligned length of plasma bubbles estimated using the fundamental frequency and Alfv´en wave speed is 100-200 km, and is consistent with the estimated based on the satellites’ dwell time within bubbles, pointing to an unexpected degree of structure along B-field lines. The final study utilizes nearly ten years of Swarm mission plasma data in the post-sunset equatorial ionosphere. The integrated power of plasma density for each 1-minute interval of plasma density measurements in the equatorial ionosphere is calculated. A similar analysis was conducted for loss of navigational capability (LNC) events. The probability distribution functions of these signals exhibited a power-law behavior, implying potential self-organized criticality in plasma density fluctuations during the post-sunset equatorial period. Integrated power for almost all LNC events is concentrated in the high-intensity portion of a heavy-tail probability distribution function, indicating that systems adhering to a normal or close-to-normal distribution would not generate fluctuations sufficiently intense to cause LNC.