The word 'very' is not a particularly good/elegant choice of words in that sentence, but I will stop short of saying you 'cannot' use it. Instead, I will say that a better word should be found -- something such as 'astonishingly' perhaps.
I suppose the use of 'carried away' is OK, but again there are other words that might be more elegant and/or more appropriate. Personally, I tend to use 'carried away' most often with a sense of 'overly excited' rather than just 'greatly excited'.
As for the singular/plural issue, I would NOT expect an American to use a plural verb with 'audience' in that sentence, but would not be surprised to see a Brit do so. I think you might see either the singular OR the plural form of the verb from a Brit. Note also that there isn't anything about the sentence that specifically suggests 'individuals' rather than the group as a whole. So, in a nutshell, the use of the singular form of the verb is just fine in my book.