Why is nouă used here? Is it as an indirect object I.e. our or is it referring to the number nine, in which case it would not be necessary here?
Here "nouă" is unambiguously a stressed pronoun in the dative case. It is optional. It emphasizes the unstressed pronoun "ne".
If the phrase would be "Nouă ne place foarte mult.", then "nouă" would be either a stressed pronoun like in the original phrase or the numeral nine, depending on the context:
Exersăm navigatul. Nouă ne place foarte mult. = We exercise sailing. We like it a lot.
Alegeți un număr! Nouă ne place foarte mult. = Choose a number! We like nine a lot.
Please also see this thread https://www.duolingo.com/comment/26129267, and the links at the end of my long comment.