It is widely known that solar activities are connected to magnetic fields on the solar surface with significant influence on the behaviour of other solar parameters. As recent solar cycles becoming quieter and more prolonged, we investigated connections, new periodicities and many other attributes within these solar cycles using various techniques. Firstly, the continuous wavelet transforms and cross-correlation procedures were applied to investigate periodic behaviour and distributions of solar flares ( (B (13351) 36.7%, C (20699) 56.9%, M (2141) 5.9% and X (163) 0.45%)) and sunspot group numbers from 1996 July to 2016 December. The flares were found to respond differently to sunspot groups. The B-flares undergo 5-years cycle and deviate when sunspots are round 100 as well as exhibit negative correlation. The C-flares constitute more than half of total flares eruptions and have the highest correction coefficient of 0.868 with the sunspot groups. A number of periodicities were obtained. The differences in their periods were attributed to the magnetic flux configurations of sunspot groups producing them.Secondly, The Multi-Taper and cross-correlations analyses were employed to study a total of 37741 soft-X ray (SXR) solar flare events and active regions following the Hale magnetic complexity definitions between 1996 July and 2018 December. The B-flares class shows no preferred active regions they associate with while the C-flares are found to originate from the β-sunspot groups as well exhibit 11-year cycle with double peaks features. The M- and X-flares shows they originated from the βγδ-type sunspot groups. The β-sunspots display the well-known 11-year solar cycle, with the double peaks feature at solar maximum. The differences in features and periodicities observed suggest that solar flares are physically connected with magnetic configurations of solar active regions.Thirdly, using the empirical mode decomposition and other techniques to estimate the long term solar magnetic activities, we found high correlations between smoothed sunspot numbers and green coronal intensity. We also found a steady decrease in green coronal emission from cycle 19 till present solar cycle that shows continuous waning of solar magnetic activities that suggest the 100-year Centennial Gleissberg solar activity cycle began descending from cycle 19. There is significant phase synchronicity between the smoothed sunspot numbers and green coronal intensity, an indication of a complex relationship between solar active regions greenline emission through the emerging magnetic flux.Lastly, the Morlet wavelet tools were used to investigate responses and periodicities of cosmic ray intensity and solar wind speed to the sunspot numbers between 1995 January to 2018 December. The cosmic ray intensity exhibits negative correlations with the sunspots while the solar wind speed does not correlate. There is a high level of phase asynchrony between the sunspot numbers and the cosmic ray intensity. The long-term trend exhibited in cosmic ray intensity designates 11-year modulation that depends largely on the solar magnetic activity in the heliosphere. A number of periodicities were obtained for each of the solar indicator indices used in carrying out the study. Key Words: Cosmic Rays, Solar Activity, Solar Wind, Flares, Sunspots, Green Coronal Intensity
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