Since the 1540-1600 time period the Navajo have raised ( and continue too) sheep, goats, horses and had dogs for sheep herding. Some people have had cattle but they have never been as popular. Before that time period, they had dogs and perhaps domestic turkeys as did the neighboring Pueblo peoples.
Yes,they raised sheep.
Yes, the Navajo people raise sheep and enjoy eating mutton. Mutton on fry bread is a favorite at any Navajo event.
sheep
The Navajo still raise sheep.
They raise them on farms
From hunting animals and farming.
Just like other Americans, the Navajo people have pets. Cats and dogs are popular. People also keep and have kept, for hundreds of years, dogs as working animals to herd sheep. The Navajo have had sheep since at least the 1600's, perhaps as early as the 1540's.
Navajo did not fish in traditional times. Eating fish and most water animals or birds was taboo. There are 300,000 Navajo today so some fish and some do not.
They grew crops and hunted animals of the area.
deer, elk, fish, , antelope and rabbits
You do not specify the kind of trap you mean. In Navajo a "booby-trap" or man-trap is dineh-ba-whoa-blehi. An ambush is khac-da. Navajo and Zuni people used pit traps for hunting animals; tye-nde is "pits where animals fall in".
we raise pawnshop, and chickens
It depends on the context. Farmers raise animals, that is, livestock. Other people who raise particular breeds of animals such as dogs or cats may be known as breeders.