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I'd be happy if someone would answer my questions. Thanks in advance.

Q1 Are the following 2 sentences correct?

A: Mr. Brown came to see you during your absence.

B: Mr. Brown came to see you in your absence.

Q2 Are the following 2 sentences correct?

C: She helped her parents with their job during the summer vacation.

D: She helped her parents with their job in the summer vacation.

Q3 Are the following 2 sentences correct?

E: I went to the museum during my stay there.

F: I went to the museum in my stay there.

Q4 What's the difference between "during" and "in"?
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A: Mr. Brown came to see you during your absence. ... while your were absent, while your absence was taking place. Shows duration.

B: Mr. Brown came to see you in your absence. ... when you were not present, in that situation when you were not present. Shows what happens in a certain state/situation, at a certain moment/snapshot in time.
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Q1. You can use either during or in.
Q2, Q3. Use only during.

in your absence is an idiomatic combination. If it weren't for the fact that it's a fixed expression, in wouldn't be a good choice there either.

It seems to me that we use in with a period of time (in a week, in an hour) to say how long it takes to do something. (I can do that job in two days. I solved the problem in two minutes.) But we don't normally use in with the entities themselves (vacation, stay) that take place over a period of time.

It happened [during / *in] [my summer vacation / my stay in London].

On the other hand, there are a lot of expressions that can use in as well as during. Many of them have to be learned as separate expressions. (during the summer / in the summer) Personally, I often prefer during in these situations.

It happened [during / in] [the war / his lifetime].

CJ