Question

Someone a few rows ahead (was, were) coughing uncontrollably, so I missed the speaker's closing words.

Answer 1

For this question, we are trying to figure out which verb fits the structure of the sentence better. 
To do this, we must first find which word the verb is defining. The subject of a sentence (except in a few rare cases) is typically before the verb, and is always a noun. 
There are two nouns in the sentence (Someone and rows). Which one is the verb expressing?

Well, let's think about it. Are the rows coughing? Somehow, I doubt it, so we're left with Someone. Someone is a singular pronoun, so the appropriate defining verb would be 'was'.

"Someone a few rows ahead was coughing uncontrollably, so I missed the speaker's closing words."
Hope that helped =)