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Hi Orestis,
Craig has given you a more comprehensive answer than I could hope to. From my reading, the Sun's energy output is higher in solar maxima due to the increase in faculae & plages. Hence the Maunder minimum was associated with a mini "ice age".
At the risk of opening the festering sore, the link between human activity and climate change is pretty well universally agreed amongst climate scientists. As far as science goes I think it is best to rely on those who specialise in the field. So while I agree that the influence of the Sun on the earth's climate is an extremely important subject, I think its for astronomers to work out the physics of the sun and for climate scientists to work out what that translates to for the earth's climate. And while there's more to learn there, I don't think there is much disagreement that any contribution of variations in the Sun's output to recent global warming is small
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