Does it use the Android operating system?

There is an early development version of Firefox that runs on Android 2.0 or higher. For details see https://wiki.mozilla.org/Mobile/Platforms/Android

Yes, it does use the Android operating system.

The latest alpha version of mobile Firefox will not run on the LG Ally, because it is not optimized for the type of processor in the Ally.

The experimental ARMv6 builds at https://wiki.mozilla.org/Mobile/Platforms/Android might work on the LG Ally.