The 2 year old is probably done laying altogether, and the 1 year old may be close to being done as well. Egg production declines after they molt ( about a year old). Although, The new environment and the noise is more than likely stressing them out, which may be keeping the younger one from...
This was a great article and helped me out a lot when I decided to get my goats (Nubians). It doesn't answer all of your questions, but it's really informative.
http://www.motherearthnews.com/homesteading-and-livestock/how-to-be-a-goat-farmer-zbcz1402.aspx
Chickens are flock animals, taking away all the other chickens is sure to stress her out. It also makes her more vulnerable to predators.
Birds are prone to depression, which may also cause her to become ill. I'd wait until she has some new friends.
Most hens don't produce as much after they molt- usually after they're about a year old. The decline is normal.
As for the dirt, I've never heard that. Chickens actually bathe in dirt, so taking that away may cause stress.
The cracked egg is probably the only one that's salvageable, but the tape needs to come off. If you leave that on, the chick won't be able to peck through it when time comes.
I've yet to see a 100% accurate method, but examining the vent is usually the best way to go. If that method is too complicated, then try the wing method. Gently extend the wing, if the feathers are all relatively even, it's a pullet, if there's a gap, or if the primary feathers are longer, it's...
My personal experience is that as long as your chicks are comfortable, there's no need to stress over it. The point is to keep them warm enough because they cannot regulate their own temperature yet, so as long as they aren't huddled together or sprawling out, you're probably doing just fine.
Put an egg (preferably her egg) into the box where you want there to lay. Show her the egg, and place her in the box. Be consistent, and eventually she will catch on. She sees other birds laying in that spot so she's doing it too, but if you redirect her to where the other chickens are laying...
I've raised other varieties of birds, but not ducklings, however, one of my doves had a similar issue after "Mom" spent too much time sitting on her. Funny as it sounds, and looked- the vet fitted her with a tiny leg splint, which stayed on for a couple of weeks and this corrected the problem...
I have a dozen RIR's, all about a month and a half old. One of which is already displaying signs of being a good rooster. (shooing the flock, pacing on the front lines, etc.)
Since none are fully feathered (still missing their head feathers), I'm sure that they're nowhere near being set in their...