Here are the terms you're looking for:
Cattle:
- The act of giving birth in cattle: Calving
- Newborn in cattle: Calf
- Mature male in cattle: Bull
- Female cattle under 2 years of age: Heifer
- Mature Female in cattle: Cow
- Castrated male in cattle: Steer
Sheep:
- The act of giving birth in sheep: Lambing
- Newborn in sheep: Lamb
- Mature male in sheep: Ram
- Mature female in sheep: Ewe
- Castrated male in sheep: Wether
Goats:
- The act of giving birth in goats: Kidding
- Newborn in goats: Kid
- Mature male in goats: Buck (or Billy)
- Mature female in goats: Doe (or Nanny)
- Castrated male in goats: Wether
Swine (Pigs):
- The act of giving birth in swine: Farrowing
- Newborn in swine: Piglet
- Mature male in swine: Boar
- Female in swine with no babies: Open Sow
- Female in swine with babies: Sow
- Swine under 120 lbs: Piglet
- Swine over 120 lbs: Market Hog (or sometimes just "Hog")
General Terms:
- Caprine: Relating to goats
- Porcine: Relating to pigs
- Ovine: Relating to sheep
- Bovine: Relating to cattle
- Poultry: Domesticated birds raised for food, such as chickens, turkeys, etc.
- Male turkey: Tom
- Female turkey or broiler: Hen
Feel free to ask more questions if you have any!