If I remove an app then will the preferences/caches/logs be deleted as wel?
No, no files are leftover when deleting an app. iOS apps (and now OS X apps too), are Sandboxed. This means that each App has its own space in disk, with its own directories, which act as the home for the app and its data.
Deleting an app from the iPhone deletes this sandbox, deleting all data associated with the app.