Does "вы" always take the "слышали" past tense?
Is there an acceptable distinction between "вы слышал" (you, formal singular) versus "вы слышали" (you, formal plural)?
No. Вы always takes plural endings, even if you are referencing a single person.
I don't think so. Russian has only one past tense so far that I'm aware of.
What is wrong with "Did you hear that?" Is it sentence arrangement? Because I thought "что" could mean both "what" and "that".
What did you hear? - Что вы слышали? Did you hear that? - Вы слышали это(то)? "That" = "Что" - как соединительный союз. I thought, that he worked hard.