Two confusions here

1) Your father wouldn't have asked such a stupid question.
Does this sentence mean the same thing as "Your father shouldn't have asked such a stupid question"?

2) She struck him across the mouth.
I am particularly puzzled by the place (as indicated by the prep "across") where he received her striking in the above sentence.
Thanks for your help in advance!

1. No. They don't mean the same thing. It's a bit hard to explain without using the "would" construction again, so I'll try to show you what it means by example.

Person A asks a stupid question.
Person B: Your father wouldn't have asked such a stupid question.

Person B is telling Person A that Person A's father would not have asked a question as stupid as the one that Person A asked. (I didn't use any pronouns in my explanation, so that it would be easier to understand.)

Another example:

Person A: My father asked a really stupid question. It was "..."
Person B: I don't believe you. Your father wouldn't have asked such a stupid question.

In this instance, Person B is expressing his doubt that Person A's father would really ask such a stupid question.

2. I believe the reason that the preposition "across" is used is that slapping is a sweeping motion, and so when you slap someone, your hand moves _across_ their mouth. Do you understand now?

I see. Thank you very much! Why not give you yourself a name, Guest? You are so kind!

In the next chapter, we'll explain the phrase "smacked upside the head." ;)