I will be specific to answering the part regarding the prediction of solar flares.
Solar flares are very volatile and dynamic phenomena associated to the breaking and reconnecting of magnetic field lines in the Sun's photosphere.
There is a phenomena associated with solar flares, called quasi-periodic pulsations, which sometimes precede a solar flaring event. As such, monitoring of such pulsations may give rise to a plausible prediction method. However, the accuracy and reliability is still to be debated.
A few good papers on QPPs:
Quasi-Periodic Pulsations in Solar Flares: new clues from the Fermi Gamma-Ray Burst Monitor
Time delays in quasi-periodic pulsations observed during the X2.2 solar flare on 2011 February 15
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