There's nothing inherently flawed about drawing a conclusion based on a sample. What would be flawed is relying on an unrepresentative sample, but that's not what (A) says. In any case, we don't have any reason to think the sample is unrepresentative.

The survey found that 35% believe officials should resign "only if" convicted. "Only if" introduces a necessary condition for resignation. But the conclusion treats this result as if it tells us how many people believe officials should resign "if" convicted. This is the way in which the author confuses a sufficient condition ("if convicted") with a required condition ("only if convicted").

No word in the argument has two different meanings. The problem isn't ambiguity. It's that the author misreads the logical relationship expressed by "only if." The phrase "only if" has a clear meaning (it introduces a necessary condition), and the author misinterprets it as expressing a sufficient condition.

(D) might be tempting, because the conclusion refers to the belief "should resign if convicted," and neither survey question directly asked about that belief. But there are a few problems.

First, the conclusion isn't about "a specific belief." It's about a comparison involving two beliefs.

Second, the "if indicted" part of the survey matches the "if indicted" part of the conclusion. The conclusion's use of the 50% figure is legitimate. The only error is in how the author handles the "only if convicted" survey result. So arguably the survey doesn't ask about "two different specific beliefs"; only one of the beliefs is different ("only if convicted" in the survey vs. "if convicted" in the conclusion).

Third, it's not inherently flawed to draw a conclusion about one belief based on survey responses about a different belief. For example, if a survey found that 80% of people believe "it will rain today," it would be reasonable to conclude that at least 80% believe "there's at least some chance of rain today." The second belief is different, but it's reasonable to think that if someone believes it's going to rain today, that those people must agree there's at least some chance of rain. So the problem in this argument isn't merely that the author moved from one belief to another. It's how the author moved: by treating "only if convicted" (a necessary condition) as equivalent to "if convicted" (a sufficient condition). (B) identifies that specific error.

There is nothing contradictory about the premises. It's possible for 50% to believe officials should resign if indicted and for 35% to believe officials should resign only if convicted. You might pick (E) because you think that there's something contradictory between the conclusion and the premises. But even if you think that, (E) is accusing the premises of contradicting each other.