I looked at the first several pages of questions, and my impression was that it looked more like a push-poll or exercise in writing trick questions than a legitimate test of knowledge.  E.g. #5 (makes no distinction between OIL and ENERGY, thus misleading), #7 (irrelevant, but aims at the emotions), and #10 (rolls the likes of oil shale together with renewables).

The authors should be ashamed of themselves.

Well, if you don't know the difference between oil and energy, I would say that is a lack of knowledge, not a trick question.

Of course, our own quiz, which steers everyone to think of Peak Oil, is also a push-poll, by your definition.

Such problems hurt the reliabilty and thus the validity of outcomes drawn from the results.

Too bad there wasn't a control group made up of people provided the information and differences in terminology and then the quiz.

I think everyone picks the questions so as to make the point they are looking for, but it seems like they have tried a little harder than most. I didn't want to be too hard on them for that, and instead tried to sum up the points that they seem to be making - and which seem reasonable to me, and which don't.

I might note that the way they were hoping that we would write this up is
"Americans' knowledge of oil is terrible. We could be making bad decisions because of this. Oil companies profits aren't really all that high, and oil companies are making significant investments in new technologies. We really aren't all that dependent on imports, either."

I couldn't do that.

These are links to a few other write-ups of the oil quiz:

Geoffrey Styles - Energy Outlook
Captain's Quarters Blog
Robert Rapier - R-Squared

I also found the API press release. I couldn't figure out how to link to it, so I will post it in another comment.

E-P, you say "#7 (irrelevant, but aims at the emotions)".

Irrevelant to what ?

One of the principal criticisms of the oil companies by the U.S. congress, newspapers, and average person is that the "oil companies" are getting big profits.

Question #7 points out that a significant share of these profits go to average people in the form of 401k returns, pensions, and other investments.

Irrelevant in general.  Significant shares of ALL corporate profits go to pension funds, 401k's, etc.  You might as well argue that the US taxpayer ought to support more wars, because war is good for the defense industry and many pension funds hold defense stocks.  It's just special pleading, and deliberately misleading to boot.

If the merits of the oil industry (such as it living off an absolutely irreplaceable one-time gift from Nature) are such that the US citizens should insist on it paying more taxes for what it gets, then it should pay more taxes.  We had this same argument around electric utilities, and decided that they didn't merit a guaranteed return either.