Yes chickens can mate with a duck.
However it's usually the male duck that tries to mate with the female chicken and if the male duck tries to mate with the female chicken it can kill the female chicken.
So if you are raising ducks and chickens they should always be kept separate otherwise the male duck could try and mate with the female chicken and then the female chicken can be killed.
Some ducks do like being pet and other ducks do not.
It's up to the individual duck on whether or not they like to be pet.
Male ducks like to be pet more than female ducks and if the ducks are pets then they may like to be pet while ducks in the wild or in a park setting may not want to be pet.
The ducks here at our park are used to humans and do like to be pet and will come up to you when they trust you.
Some ducks do eat their own poop.
I've seen some ducks eat their own poop at a park here where they have ducks and after the duck pooped it would turn around and eat it.
Then another time I saw another duck come over and eat another ducks poop.
However not all ducks will eat their own poop or others.
Ducklings may also eat their own poop sometimes as well.
The lifespan of domestic ducks is between 5 years to 10 years depending on the type of duck.
Some ducks live longer than others depending on the type of the duck.
Mallard ducks live on average of 5 years to 10 years but they may live a bit longer.
When ducks are in the wild they live at most 5 years but the wild duck may only live as long as 3 years if it becomes unhealthy or gets hunted and killed.
Ducks live much longer as pets or in captivity than they do in the wild as long as the duck is taken care of properly and fed properly.
In the wild the duck may be more prone to disease and may get killed by either hunters or other predators.