Hey,
I have got 8 Muscy's and have this problem. It's nothing to worry about and your doing nothing wrong for a start.
Your female is not ill, only broody. Muscy's go very broody and are used commonly for incubating other ducks eggs.
The fact that she makes alot of mess just after leaving her nest is because of her sitting on her nest for a long period of time... she can't go to the toilet regularly (as the eggs will go cold).
Many females 'fluff' their feathers up and also make cheeping noises. Im not sure really why they do it, but it seems normal and natural to them. Most breeds of ducks that go broody do this.
As for her eating, my females go off their food for awhile and lose abit of weight, again it seems to be a common thing.
Try tempting her with foods such as lettuce, grass, worms, snails or bread (although not too much in one go, as it swells up inside their digestive tract).
How old is your female? Is this the first time you've known her to go broody?
It may pay, if you haven't had any experiance of this before to get as much research done as possible before the ducklings hatch.
There are some very good books available such as;
Ducks and Geese - A guide to management - By Tom Bartlett
The Domestic Duck - By Chris and Mike Ashton
Poultry and Waterfowl Problems - By Micheal Roberts
Ducks and Geese At Home - By Micheal Roberts
As for you other female that is laying eggs with thin shells, feed her calcium supplements.
Egg shells are mainly made from calcium, and any problems with badly developed eggs could lead to many problems such as egg-binding.
Most pet shops should sell a suitable supplement that contains calcium, and always ask the pet shop owner for instuctions and advice.
Hope this helps abit, Mel X