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This article will help you with growing sweet potato slips.

https://www.gardeningknowhow.com/edible/vegetables/sweet-potato/sweet-potato-plant-starts.htm

Yes, they are edible.
These articles will help you.

https://www.gardeningknowhow.com/edible/vegetables/sweet-potato/are-sweet-potato-leaves-edible.htm
https://www.gardeningknowhow.com/edible/vegetables/sweet-potato/grow-sweet-potatoes.htm

Yes, this link will help you.

https://www.gardeningknowhow.com/edible/vegetables/sweet-potato/are-sweet-potato-leaves-edible.htm

My sweet potatoes were growing great. Recently looked at the bed and noticed a hole in the middle of the bed where leaves used to be. The leaves were eaten off the stem. I don't know what caused it. I found one tobacco hornworm close by. Could it or a rabbit have done this? Or is it something else entirely? Also noticed beetles or other insect starting to eat holes in the leaves as well.

You can, but I don't advise it. You may wipe off any extra dirt, but don't wash them until you are ready to use them. This will help give it a "protective" layer. Here is an article for more information: https://www.gardeningknowhow.com/edible/vegetables/sweet-potato/sweet-potato-storage-tips.htm

The best way I have found to ensure that your crop is the exact same the next year, is to take a cutting of the plant you want to keep dip it in a mixture of a few drops of honey, a crushed aspirin tab, and just enough warm water to get it to mix into a paste. Dip the cut end into this, and mix the rest with water. Water the soil with this until it is moist. You will have rooted plants in 1 to 2 weeks. Keep these indoors in a bright, south-facing widow, or under horticultural lighting.