Quite right: if you move app files with a file manager you'll break the app.There is a file manager named x-plore that is very feature rich and will show hidden files, but I wouldn't recommend moving apps with it.
To anyone who is tempted, it's obvious if you think about it: if the app developer wrote the app to store its data in a particular folder and you move that folder somewhere else, the app isn't going to know to search your filesystem for the data, it will just see that its data are missing.
The same is true for the app itself: if you were to move the app (or parts of it) using a file explorer (which requires root) the operating system wouldn't be able to find it any more.
There are ways of doing things like this using root, but they are a bit more involved than just moving an app's folders to where you'd like them to be (they involve adding an ext filesystem partition to the SD card and setting up symbolic links, usually using a script or app to automate this as well as mount the extra partition at boot-up). That's what we used to do before the ability to partially move apps to SD was added in Android 2.2, but while it should still be possible it's largely forgotten these days.