Welcome, Australorps are great birds. Have some myself and found them to be easy going, not overly aggressive and easy to handle /get used to owners. Have fun!
Wash and put in the fridge, should be fine. Over time your pulleys/hens will improve. Every now and then I still get an egg that I shake my head at.... covered in poop and somehow not even close to the nesting box.
I would recommend a wash to remove as much dirt and feaces as possible. If the feathers are clinging to each other, depending how bad, dirty, close to their skin it can cause issues such as fly strike, irritation to the skin, restrict full range of movement and irritation.
Depending on your...
Welcome, hope you find some great friendly advice here. I see your family has the chicken math bug!
I have to restrain myself, there are too many lovely breeds but really such a limited ability for me to keep more than about 14:( I think I need a farm haha
I have thought about the d’uccle.... are they much smaller than Other bantams? I can always house them separately, I have a second unused coop at the moment.
Not really a fan of silkies, but may be open to giving them a go.
I guess it may end up being what we can source.