RK Squared runs as a proxy: It runs on your PC and Mac, and you configure your phone, tablet, or emulator to connect through it, so that it can track your game status.
Both Android and iOS versions of FFRK are supported.
Both the global (GL) and Japanese (JP) versions of FFRK are supported. However, a running copy of RK² only supports a single FFRK profile, so trying to use one copy to track both GL and JP will cause confusion.
FFRK for iOS encrypts its data, so, in order for RK² to work for iOS, it needs to be able to decrypt HTTPS traffic. As a general rule, you should be very cautious in granting software the ability to do this, and you should only do it with software you trust. (RK² is designed so that it can only decrypt FFRK traffic, which should help with any security concerns. In technical terms, it generates a private CA (certificate authority); then it uses that CA to create and save a certificate for ffrk.denagames.com, so that it can decrypt FFRK traffic; then it discards the CA key, so that it can't create certificates for any other sites.)
RK²'s information about soul breaks and legend materias is currently not automatically updated outside of new releases; it's just a snapshot of whatever was available at its last release.
RK² currently only supports a single FFRK profile. So, for example, if you play both GL and JP, you'll need to find a way to run two copies of RK² (for example, use two different laptops, or two different PC accounts, or manually copy RK²'s config.json depending on which profile you're playing).