The question's too broad to give a specific answer to, but here goes:
1. If you deleted an app, your recycle bin is the app store, since you can get it back for free from there. Whether or not all the data you had saved in that app returns, depends entirely on the app developers and whether they store it locally on your phone, or in a cloud.
2. If you deleted an individual file from an app, it depends entirely on the app. Some may have a recovery option, others don't.
3. If you deleted something using an actual file manager, like iFile on a jailbroken iPhone, all deleted files go to /var/mobile/Library/iFile/Trash/, but only if your settings had that option enabled.
EDIT: I started typing the post before you mentioned the contact issue, hence my apparent lack of comprehension.