Learn Russian: Из-за свиста и волнения мне совсем не думается. - Because of the booing and nervousness, I can't think straight at all.

Using the dative pronoun мне with a reflexive verb like думается creates an impersonal construction. It implies a lack of conscious control, as if the action is happening to you: thinking just is not working out for me. While я не могу думать simply states a factual inability, мне не думается captures the psychological block caused by the nervousness.

Does свист really mean 'booing'? I thought it meant 'whistling'.

It does literally mean whistling. However, in Russian culture, whistling at a performance or event is a sign of strong disapproval, which makes it the exact cultural equivalent of booing in the English-speaking world.

The current lesson is about несмотря на (despite), but here we see из-за. How do they differ grammatically?

Из-за means because of and points to the direct cause of a situation. It always takes the genitive case, which is why we see the endings in свиста and волнения. By contrast, the lesson's target несмотря на means despite, showing a concession rather than a cause, and it takes the accusative case.

Why does думается have the -ся ending here if thinking is not an action you do to yourself?