My app needs to save and retrieve images from root dropbox folder (not my app's root folder under dropbox), currently I setup my app in App Console with files and detesters, need access to files already on Dropbox and specific file types for images.
Which type of dropbox api should I use ? Core API or Sync API?
You want to retrieve files from Dropbox then you need to use Core API of Dropbox. For better use you need to read
https://www.dropbox.com/developers/core/start/iosthis. This is a good way to retrieve specific files from Dropbox in your case.