When you set the equalizer on iTunes does the equalizer stay that way on the iPod even when you have the EQ setting on the iPod turned off?

The equalizer is a playback effect, and does not effect the file. When you transfer it to your iPod, the EQ setting does not transfer with it. If you want to EQ when you listen to it on your iPod, you will have to edit the file (using Audacity or some other audio editor) or turn on the iPod's own EQ.