It is possible that solar storms could affect the electrical grids. I don’t think it is likely that the whole world would be affected, but large parts could be. However, a study by Penn State (where I graduated) suggested that solar flares could cause major disruption just by causing problems to as few as 2% of grid power stations. The reason has to do with the sensitivities to space weather disturbances of the complex electrical apparatus that power stations are.
Yes, massive solar flares can be disruptive – and have been in the past – because they bring a huge flux of very energetic radiation with them. Usually our magnetic field deflects the solar wind, but large flares can partially overwhelm the capacity of the magnetic field to protect Earth’s surface.