I believe are called incubating birds, because they are incubating the eggs!
Incubating the eggs was necessary for their survival.
incubating eggs means keeping them warm ready to be hatched
If she has definitely stopped sitting on the eggs, then throw them out.
Actually you can as long, as you don't handle them to long.
They look the same as normal eggs but the things inside are different.
shivering thermogenesis
None.
Setting eggs is the term for incubating, whether done by a broody hen "setting" on a clutch of eggs or by artificial incubation.
There is disagreement about this. It most depends on what you use your hen for. If you use them as incubating machines, then no (she might not go broody as often). If you are selling hatching/eating eggs, then yes, it should be discouraged.
You simply remove her eggs, keeping her from setting and incubating them.
No, not if you want the bird to return to incubating the eggs.