use will, would, shall or should appropriately [migrated]

Solution 1:

I'm not sure in what way you "test" your answer with an ebook, but if it accepts or gives only one right answer for a question that might have more than one right answer, then maybe the given answer is only one example of several possible ones.

• I find it astonishing that the old theater will be demolished! —This is perfectly valid. In this sentence the speaker has learned that there are real plans to demolish it in the future.
• I find it astonishing that the old theater would be demolished! —This is also valid. In this sentence, the plans to demolish the theater might be really planned, or might just be being discussed and imagined. Since we are given only this one sentence, there's no context to say whether "will" or "would" is the better choice.
• shall, should: These are also valid choices, but shall is rather archaic and unusual in modern use. It works as an old-fashioned version of will. Similarly, in this context at least, should works the same as would, and is not archaic, but a bit more formal.

• Thanks for the offer of a lift, but to be honest, I would sooner walk. This is valid and makes sense. None of the other choices fit. Why? This sentence talks about your preference, something you would like to do, and uses hypothetical language. In this context, sooner doesn't mean "more soon," but means "prefer to." You could use other words, but you would have to change other parts of the phrase:
• Thanks for the offer of a lift, but I will walk. This is certain.You couldn't use will in the example with sooner. Since will won't work, neither will its equivalent shall.
• should: Here substituting should for would makes the sentence sound even more archaic than in the first version. "I should sooner walk" is valid but outdated.