I would translate のこと as 'regarding' or 'about'. It shouldn't really change the meaning but is just a slightly more indirect way of saying 'the weather will be x'. Maybe you've also heard of あなたのことが好き(すき)です as a way to confess your feelings. The meaning should be the same as あなたが好きです but it might be perceived as more indirect and polite I guess.
Technically speaking, pretty much all of our power is solar power with extra steps.