OK, so this one is tricky to explain but in the end the simple answer is "Yes, you CAN move apps to SD BUT it's not simple and it does require root".
So, first the basics: Google decided to remove App installation onto SD cards from Android 4.0 upwards. Why they did this is still on debate, but alas, they did. No way around it. Main app has to be installed in the phone's memory but the app developer can implement 'extra downloads' going into the SD card (like a game, for instance, in which you download a small app and then it prompts you to download an additional 3GB of data). The problem is most developers don't bother to code this in and all that truckload of data ends up eating away your precious internal memory. Again, this was introduced with JellyBean (Android 4); anything before that is different.
As always, rooting your phone gives you access to EVERYTHING in it, and that means you can tamper with the code itself. In order to be able to use your SD card, you have to 'fool' the phone into thinking it's part of the internal memory. You do this by mounting the SD card's partition as part of the internal one. I'm sure there are guides on how to do this in the forums but, unfortunately, I don't know exactly how to do this since I've not rooted my phone (I want to keep my warranty intact for the time being).
BTW, the apps listed above all bear an incompatibility warning with Android 4, so that's probably why they don't work with your Note 2, even if rooted. (Don't know why it lets you install it, though...) And most of the apps that require root also state that they require "Busybox" installed (whatever that is).