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Just replant what you dug up. They are pretty tough and it should grow. Keep it watered till it gets established.

There will, certainly, be leftovers that pop up! Daylilies can be quite prolific, so killing any remaining pieces of the rhizome will be important.

Fortunately, it is not difficult to do so. Here are two articles that will help you to accomplish this:

https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

https://www.gardeningknowhow.com/plant-problems/weeds/boiling-water-and-plants.htm

They don't look healthy. I would check their refund policy and call and let them know you don't like the look of the roots. They may ask you to plant them and if they don't grow properly, give you a replacement or refund next spring if they don't grow well. A reputable nursery will want you to be satisfied with their products.

Daylilies are not true lilies but you are right. Members of the Hemerocallis family are edible.

I will suggest an article regarding that fact.

Those ARE seed pods, and you can plant them when they are ripe, and opening on their own.

https://www.gardeningknowhow.com/ornamental/bulbs/daylily/daylily-seed-propagation.htm

One of my daylilies didn't bloom last summer then this season it bloomed like crazy. And I don't think I added any fertilizer last spring. If your stand of daylilies has been there a long time, it may need dividing. Here is more:

https://www.gardeningknowhow.com/ornamental/bulbs/daylily/no-blooms-on-daylilies.htm