Word choice - Grammar! [closed]

In the first question "is" is strictly correct, the subject (team) being in the singular. This rule is less observed than it was and may feel somewhat formal now.

Only the team with the lowest service ratings is referred to training with human resources.

(I'm surprised to see "human resources" used in 1972 when "personnel" was more common.)

In the second question I think "who's" is correct for the reasons you give.

The person whose engine is sputtering is usually the person who's most inclined to visit the mechanic.

But the sentence seems too long, considering how little is being said. And the repeating sounds person whose ... person who's is weak.

It might sound more natural if we leave out "who's":

The person whose engine is sputtering is usually the person most inclined to visit the mechanic.

We might also get rid of the second "person" and say,

The person whose engine is sputtering is usually the one most inclined to visit the mechanic.

Either option in question three would be grammatically correct. There is nothing to choose between rapidly and quickly, but the word about suggests a scattering rather than a steady progression. I prefer "spread quickly through" or "the fumes quickly filled the room."

I believe your analysis to be correct for all three.

I need not repeat all the definitions in the Cambridge dictionary but through has the connotations that you suggest.

Cambridge dictionary

I suspect the compilers of the questions were testing for understanding of the difference between through and throughout.

Throughout = in every part, or during the whole period of

Cambridge dictionary