The expected rise in the price of oil could be a serious impact to

There's a big difference between being an impact (choice A) and having an impact (choice E).

In choice A, "to be an impact" means "to be the effect or result," but in this context, the "rise in the price of oil" is the cause, not the effect or result.

Since "the rise in the price of oil" is a cause (not an effect), it makes more sense for "the rise" to HAVE an impact (to cause some effect or result) than to BE an impact/effect/result.

That makes (E) a better choice.
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The expected rise in the price of oil could be a serious impact to industrialized nations and severely diminish the possibility to have an economy free of inflation.

(A) be a serious impact to industrialized nations and severely diminish the possibility to have - idiom error. an impact on is correct
(B) seriously impact on industrialized nations and severely impede the possibility to have - same as A
(C) seriously impact on industrialized nations and severely impede the possibility of having - same as A. Usually seriously impact + noun would be correct
(D) have a serious impact on industrialized nations and severely impede the possibility to have - first part is okay but the possibility to is not the correct idiom here.
(E) have a serious impact on industrialized nations and severely diminish the possibility of having - No error and idioms are perfect. Hence Correct.