If an image is edited does it change in a shared album?

That is right. When you share a photo, a copy of the photo is added to the shared album. The copy will stay in the album just as it is, even if you delete the original from your photos library or edit the photo.

The shared albums are using a different part of iCloud, that does not count against your subscribed cloud storage and is free. It is completely independent from your cloud storage. You will have the down-sized versions in the separate storage for shared albums and your originals in your main cloud storage.