Hi Emily,
It depends on how you want to handle the existing app in the store. If you want to replace your existing app then you can use the folio migration tool in DPS 2015 to migrate all your old content over, create a new app, and submit that new app to the store to replace your old one. Your readers will get the new DPS 2015 experience but will still be able to access the old content (now as collections migrated to DPS 2015, rather than folios in the old app). This option is available for iOS at launch, and will work with Android and Windows shortly after.
2) There is no library anymore. Instead the reader sees browse pages and cards. You get to decide the structure of your app using browse pages and cards. If you want a simple view of what you used to have as folios, you just build a collection that has your back issues in it and do a layout/card you like to display them.
3) The analytics systems are separate. The new app will be a new analytics instance and will not have the data from your legacy app in it.
Hope this helps,
Neil