If a duck egg has a little crack in the shell will it survive and there were noises coming from it when put it up to ear so think it is alive How do take care of this egg?

Not generally. If bacteria enters the egg and destroys the developing baby, then no it will not survive.

This all depends on how big the crack is. If it is large and you can see inside then hell no, the bird is doomed by infection. Doesn't matter what kind of bird.

If the crack is only small/a hairline fracture then there is a hope under the right conditions. What is vital is that the rubbery membrane underneath the hard shell is intact. If this is intact there is actually quite a lot of hope. If the egg is cracked but you can see this membrane has not been broken then i would for extra safety and best possible chance of survival gently spray or wipe the shell with a germ killing barrier of hand sanitiser then cover the crack up with a smally square of masking tape.

If the crack is larger and the membrane is broken then the bird will most certainly perish. There is a small chance the bird under this scenario can survive if it are just about fully developed. You can quickly wrap the egg up in cloth and take it to the vet and sometimes birds can be saved by being extracted from the egg prematurely then put into intensive care. good luck