If (A) looks appealing, read the conclusion carefully: it's talking about what Astorga intends to do, whereas (A) is talking about what she can do. Astorga's actual capabilities are a different issue from her intentions: she could intend to do something impossible, or intend not to do something possible. So it's not necessary to assume (A).

The conclusion doesn't depend on the polls being accurate or inaccurate; it just depends on Astorga's promises being different from her actual plans. Even if the polls are 100% correct, that wouldn't harm the argument, meaning (B) isn't necessary.

The conclusion is limited to what Astorga intends to do if elected. The likelihood of her actually being elected doesn't matter, and neither does her ability to persuade voters. The author is just trying to convince us that Astorga is lying, not that she'll win.

Astorga’s personal opinions concerning the role of a mayor are irrelevant, because the conclusion is about what she intends to do if elected. Whether she's making these plans because of voters' wishes, because of her own opinions, or for some other reason doesn't make a difference. So it's not necessary to assume anything about her opinions.

This must be true in order for the conclusion to follow. If we negated (E), and Astorga intended to do what voters want once she’s elected, then her campaign promises would be truthful. Taking away (E) would make the argument fall apart, which is how we can tell it's necessary to assume. And this assumption is certainly questionable: we have no reason to assume Astorga's intentions.