My native intuition agrees with your own: it's a pretty poor use of "whereas".
Whereas "while" can have a broad catch-all conjunctive meaning like that of "and", "whereas" strongly suggests either contrast or the furnishing of a reason (consider legalese for proposing a motion). While "whereas" and "while" overlap, the overlap is not this complete.
To be less coy, (e) as the answer puzzles the reader because the two clauses are obviously not in contrast and less obviously not in a "because/therefore" relationship.
Whereas at least one commenter agrees with the intended answer, I would go so far as to say that while it's the least wrong of the options provided, it's still wrong and suggests a writer who (like so many) hasn't really grokked the uses of "whereas". I would certainly not let it go by as an editor.
The second question is whether "while" could be replaced with "during the time" here. There are two answers to give:
It can't be replaced syntactically. The syntax would only work if you said "During the time that".
Even then, it can't be replaced semantically. For this sense to work, "during" has to be durative. There has to be an identifiable timespan during which two things can happen simultaneously. But neither "the novel captures the daily life" nor "the novel is a wonderful guide" have this aspect.
The phone always rings while I'm in the shower.
Note that you should not confuse this sense with the one in a sentence like this:
The novel captures the daily life of the city in the 1940s while also serving as a wonderful guide to the cuisine of Salvador.
This is not really "during the time", but the broadly conjunctive "and" I referred to earlier.