Admins can fly because they have /fly. Hacks are allowed unless it doesn't damage the server. If it did, they would be banned. You can fly on hacks, almost any hack, but NCP (No Cheat Plus) prevents you from doing so.
You can use any hack. But I recommend Resilience or Iridium. You can tune the flight speed in the GUI to make you faster. But make sure to have /fly and /sp speed turned on. If you use Iridium turn it down to 0.7 speed. As for Resilience.. I'm not sure. You can get your hacks at wizardhax.com and find tutorials on youtube to help you through the process.
What client are you using? Don't turn on the speed hacks. Tune your fly speed and make it quite low. Also, make sure you have /fly AND /sp speed on.
I don't know, but if it's not on, you can't fly as fast. If you look at the speed hackers, they are always shifting.