"What percent of alchohol is beer" is correct, the "of" says that it is part of it

"What percent of alcohol is beer," is incorrect. It implies that alcohol contains a certain amount of beer, which it the opposite how how it really is. The other sentence is basically ok. To avoid possible confusion you could say something like. "What percentage of alcohol does beer contain."

I would say "what is the percentage alcohol of beer?" and "what are the alcohol limits for driving?".