I have an app which I would like to be able to upload files to. I could imagine serializing the data, putting that into an array, then serializing the array and putting that
I believe you're not very much familiar with Core Data yet. I would strongly suggest to dive into Core Data documentation.
Anyway, from what I understand, possible implementation of your data model could look like this:
Your user would have an NSSet of File objects, each File object would be responsible for storing the name and its URL in Application Documents directory.
As for your second issue, I don't quite see a question there.
Hope this helps, Cheers!