Barn, stockyard
cow
Heifer
There really is no such thing as a male cow. Cow is female and Bull is male.
A female cow is called a "cow" - if it has not given birth it can be called a "heifer". Perhaps you were thinking of a "cow" called 'Daisey'.
A 'cow's home' would commonly be a barn, cow-shed, ranch, or etc. They require a shelter to withstand various weather.
That would be the udder.
Either cow towns or stockyards.
what is the name given to the home of beaver
A "cow" is a cow when that "cow" is a she and she has given birth to at least one calf.
Vaccination
Bulls
It's called 'Colostrum'.