I own an iPod nano i10s. How do I download music to it now that I've replaced my desktop with an iPad Air?

You can use the iTunes app to transfer music.

See Page 15 of the iPod nano manual here > https://manuals.info.apple.com/MANUALS/1000/MA1624/en_US/iPod_nano_2015_user_gui de.pdf

What is an iPod Nano i10s? No such Apple device name exists, its simply iPod Nano.

http://www.apple.com/shop/buy-ipod/ipod-nano

With that said however, iPads are not capable of syncing music to iPods or any other music device really.

iPads themselves sync with computers to get their music.

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