Does iPod need wifi to play music?

If you download the music onto your iPad where it's stored on your ipod, then no. if you're wanting to use the radio feature, then yes.

one way to test, download a song, put your ipod into airplane mode - which turns off its antenna and simulates no wifi - and play your music.

To turn on airplane mode, swipe up from off the bottom of the screen. This will 'pull up' the control center. you'll see a little airplane symbol. Tap on that to turn it on. You could also simply turn off your wifi by tapping hte little wifi symbol.

Alternatively you could go into the settings, and turn on airplane mode or turn your wii off.

https://www.apple.com/support/ipodtouch/

A link to file away for later. there are a lot of how to's and tutorials there.