The eggs are "off white"
If the Mandarins are in with chickens, and no other ducks, compare the eggs you think may be Mandarin to any old chicken egg. Chicken eggs have a coarser surface, with larger pores than waterfowl eggs. Waterfowl eggs almost feel "greasy" and have very small pores.
You cannot free range them, it will not work unless the birds are imprinted, even then...only slight chance.
I do not recommend pinioning cavity nesters.
For MBTA listed species of coot, gallinule, rail, etc, you will need a USFWS special purpose permit as well as whatever your state requires. You must have the permit before getting the birds. If you are serious about getting into "shorebirds" Google Spurwing or Lapwing Plover or African Black...
May be referring to a LA state law. The sale and disposal permit satisfies Federal requirements for MBTA listed waterfowl only. Check your state "Game & Fish" dept. laws for additional requirements. EX-In my state I am required to have a "domesticated bird breeder permit" in addition to the sale...
Is the bottom of the air sac horizontal across the egg shell, or is is starting to angle? When it starts to angle (about 30 days) that is when they are close. Do you see movement, or possibly a bill protruding into the air sac?
Either leave it on constantly so they have to get used to it, or get rid of it. If you are hoping to breed this spring, get rid of it. Adding stress factors during the breeding season is detrimental.
Red Breasts are charming little geese. They are getting really loud right now for breeding season. The gander is also getting aggressive. The aggression is comical because they are so small. Median going rate is $1000/pr, I would not spend more than that.
Take the bird to the marsh area where you have seen wood ducks and release it. Preferably before all the other wood ducks begin to migrate (ie very soon). You do not want to get visited by a Fed warden for having that bird either.