The only emulator I have is ZSNES and I want to know if I am allowed to use it or if I have to get another one to play in any categories. I specially want any % and glitchless any% US

Typically, ZSNES is globally banned in speedrunning, due to it's notorious inaccuracy. Thus, not allowed for FFVI as well. For SNES Emulators, SNES9x is the most easily accessible SNES emulator, and anything over version 1.5 should be good - though there are others as well.

If you're looking for a good reference of what is generally allowed for emulators for most games, you can usually refer to: http://www.speedrunslive.com/faq/ "Can I play on Emulator" and it'll be accurate most of the time.