Dear Kasia,

Thank you for sharing your experience. I would say that all types of analysis are mostly done to make a prediction about a group because we usually want to generalize the results to a population.
The only reason to study individual subjects would be that one want to make predictions only in those particular subjects. That being said, the purpose of "2nd level analysis" is so that one can make a group prediction and not on one subject.

Also, I think in GLM implementation, the variance terms used are for "mixed-effects", that include both fixed-effects and random effects. That is so that one can generalize their results.

I hope someone else can verify.

Best,

Zaeem