What is the .android_secure Folder?
android_secure folder contains those apps which you have moved to external SD. Files inside them would have .asec extension
Android 6.0 upwards don't allow you to move apps to external SD as you have been doing. They use adoptable-storage wherein the external SD card and internal storage are merged to create a bigger storage. You can read more in adoptable-storage tag wiki. This folder is of no use to you in migrating , since the concept is different ( best is to restore all apps to internal storage before attempting backup )
Coming to the migration of apps and data,


If your device is not rooted, it is not easy or guaranteed to work since you are jumping across two versions ( this could be a separate question )
If your device is rooted , titanium-backup or nandroid backup would help