You can't transfer songs from an iPad, iPhone or an iPod Touch to an iPod Nano. You have to sync the music to the Nano using iTunes on a computer. In order to do that, you need to transfer the music from the iPad into your iTunes library on a computer. You could also download the music into the iTunes library as long as you use the same Apple ID that you bought the music with originally.
Do you have a computer running iTunes? You need to be running at minimum, Windows 7 on a PC, or OS X 10.9 on a Mac and you need iTunes 12.5.1 as well. If you don't have a computer, it doesn't matter because this is the only way to accomplish what you want to accomplish.