This seems to be another example where we've lost the leading 'в' from the slow version of the audio. Or am I just mishearing? I'm still at a level where I'm using the slow version for most exercises, so I transcribed it without the 'в', and got it wrong. I also wondered why the sentence didn't make sense, as it sounded something like: "The shop was not a plate". Once you realise it should have been: "in the shop", it all makes perfect sense.
Often the 'в' (plus 'с', 'к', 'о', pretty much all prepositions) get stuck onto the next word. В + аэропорту = "ваэропорту". С + молоком = "смолоком". Words that begin with an unvoiced consonant make 'в' do the same. So в + комнате = "фкомнате". Don't forget that some consonant clusters cause the addition of the 'о'. В + Франции -> во Франции = "воФранции".
Таре́лок is genitive plural.
Не бы́ло is indeed singular. It's used instead of нет in the past tense, and it doesn't change its form.