Is it possible to read/write/delete the data present in files or folders created by other applications? I am 99% sure that Android OS does not give such permission but to be 100% sure, I want to know this. The whole context is that if I download an Android app from an external source, what kind of security threats I may have?
Is it possible to read/write/delete the data present in files or folders created by other applications?
That depends on where the "files or folders created by other applications" reside.
Files written by an app to its portion of internal storage are not accessible by third-party apps in general. Users who root their devices can arrange to access those files.
Files written by an app to external storage are accessible by other apps and by the user, though the apps will need READ_EXTERNAL_STORAGE or WRITE_EXTERNAL_STORAGE permissions.
Files written by an app to its portion of removable storage, on Android 4.4+, are not accessible by third-party apps in general. Users will have access to these files, if not through Android apps, then by moving the media to some other hardware (e.g., notebook PC).
Files written by an app to removable media prior to Android 4.4 -- through undocumented and unsupported means -- are accessible by other apps, in addition to being accessible by the user.