You could but I don't see much point to it since she will get rid of it anyway when she grows feathers. If you do want to get rid then fill a small container with warm water and soak her behind. It will loosen it enough to get it off. :)
Oh and if it's your first time with chickens I recommend you check out the learning centre, it's full of great tips and advice :
https://www.backyardchickens.com/a/
Yep, it's the same with the breed I'm afraid. Many breeds of chickens look alike when they are chicks.
Your 'fuzzy footed one' is probably a Cochin because that is the most common feather footed bantam you can get from TSC. :)