What do they do with all the food that doesn’t get eaten?

There's not much leftover, as they are served in small little sauce-like plates. It's pretty frowned upon to ask for more banchan if you aren't going to finish it.

But yes, the leftover dishes are thrown away.

A substantial restaurant meal in Korea is usually served with several standard side dishes. Due to the expense and effort of providing these to each table, restaurants often require a minimum party size of two. Also, I'm not sure if it's illegal or just gross, but if a dish looks untouched, sketchier places will sometimes just pass it along to the next customer.

Usually there isn't much. The plates are tiny and mostly have vegetables.

You eat them.