(3) Things.
(1) Yaks (and other animals that need to eat) require grasses. Grasses grow on the surface, but also on rough stone floors or underground soil, but only if you've breached the caverns (the mosses then start growing randomly, but will eventually fill everything out nicely). Look on the wiki to see how much pasturage different animals need.
(2) Butchering is done at the butchers shop. Once you designate the animal for butchering on the Z Animals screen, a dwarf with butchering enabled will come get the Yak and take it to the butcher shop, where it will be promptly struck down. Be sure to also have a tanners shop nearby, so a dwarf with tanning enabled will take the raw skin and tan it. Waste not and all. A word of advice: Put the butchers shop in a room with a door, that way if your haulers take too long getting to the meat, the miasma won't go beyond that room.
(3) All land animals use the same pathing. If your dwarf can traverse it, so can a moose, a goblin, and a cat. You can block animals movement by assigning them to a chain (they can move to adjacent squares), a cage (they get shoved in the cage) a pit (it just dumps them off the edge, if there's a path out, they can take it), or a pasture (they won't leave it voluntarily). You can also block movement by "tightly closing" doors -- but they can still follow dwarves through when they pass through it.
Long story short: Eat the yak, get chickens. They don't need pasture. Once you've secured aboveground pastures, or have breached the caverns, then you can start worrying about livestock like cows.