The current generation is ... (AE)

I think BE uses plural here, though.

BE would also use singular here - although there are lots of other collective nouns where we'd use the plural.
But which generation is meant - there are often three (or more) generations of one family alive at any one time.

Generation can be singular or plural ("is" or "are") in BE, but more commonly singular.

And "now-living" is not possible as an adjective here without sounding extremely odd.

Fully agree with #3.

Shouldn't there be "were" or "have been" at the end for the "former generations"? Coming from the German
"Die heutige Generation ist viel unhöflicher als es frühere Generationen waren."
I miss that in the English sentence.

@5 - "have been" doesn't really work and "were" is not necessary, no.

Agree with #6. Indeed, it's preferable to leave out "were".