1. Rooting has nothing to do with moving apps to the SD card. Maybe the app you're trying to use needs root, but Application manager (which comes with Android) will move the same apps. (Most apps today
can't be moved to the SD card, because they won't run from it, so the developers turn off that ability in the app.)
2. Check on
XDA Forums for rooting methods for any phone/Android version combination. (The Android version is important - you can't use a 4.2 root method on a phone running 5.0. The exact model number of the phone is important too - using a method for a similar, but not exactly the same, model could brick the phone.)