Yes. You will need to download djay (full or free trial) to your Mac in order to run djay Remote on your iPhone/iPod touch.
Make sure your iPhone/iPod touch is connected to the same local Wi-Fi as the Mac you want to control.
Make sure you are running the newest version of djay (3.1 or later).
Yes. You can always create a local Wi-Fi network yourself on your Mac through the Airport menu > Create Network... Then join this network on your iPhone/iPod touch through Settings > Network.
Yes. djay Remote gives you full access to all the songs and playlists of the iTunes library on your Mac. You cannot access the iTunes library stored on your iPod touch or iPhone.
djay Remote mimics djay's acclaimed interface and gives you instant access to your entire iTunes library and full control over nearly every feature in djay, including scratching, crossfading, Automix, Automix Queue, bpm sync, pitch bend, cue points, eq, volume, looping, skipping.
Yes. You can turn Automix on and off, add/remove songs from Automix Queue, trigger transition to the next song and more.
No. djay uses a secure network connection and will ask you for permission before allowing any device to connect to your djay.