[said in deep Morgan Freeman voice:] Only you can answer whether to diagram a logical reasoning question.

If it's helpful, go for it. But if you "get" the structure of an argument, it usually isn't necessary to diagram. For this one, it seems like you got it.
The conclusion is that the Professor isn't teaching 2 French intro classes. Why? 1. Because nobody can teach more than one intro class. 2. There aren't any intro classes being taught!
We're looking for a match - an argument with a conclusion (and preferably one about something not being true) that is independently proven by two premises. And that's (D)!
The conclusion: The new building will not be taxed next year. Why? 1. Because it has a large public space, and new buildings with large public space are exempt from taxes for two years. 2. All new buildings will not be taxed for five years.
(A) is a total mis-match. The structure of (A) is a single chain (there's only one supporting premise). Occupied by May --> Taxed by new rate, Morrison bldg occupied by May --> Morrison bldg. Taxed by new rate.
(B) is very tempting! The conclusion - that the code does not apply - is valid since the building was built in 1873, and thus before 1900 (triggering the first premise). However, the other premise does not independently prove the conclusion. It only allows us to infer that the the first part of the code will not apply. Perhaps the rest of it does.
(C) is similar to (A). The argument is a single chain.
(E) is also a single chain: hospital --> exempt from property taxes --> charged at special rate. Where's the second line of reasoning that supports the conclusion?
Does that clear it up?