Yes they do. Cows giving milk is as natural as they come: ALL female mammals, after giving birth, produce milk.
Today, modern dairy cows are bred specifically to produce large quantities of milk. Like humans, cows only produce milk after they have given birth, and dairy cows must give birth to one calf per year in order to continue producing milk. Typically they are artificially inseminated within three months of giving birth.
Yes all cows give milk (referring to "cows" as the mature female bovines that have given birth to at least one calf, not the colloquial term for "cow"), and yes they can only give milk if they have recently given birth. To confuse the reader even more, the answer to the first question would be "no" if one were to use the word "cow" in a colloquial sense, which would still make the answer "yes" to the second question since those cows that are capable of giving birth are the only ones that can give milk. The male cows (there are really no such things, but I'll keep going anyway) cannot give milk nor give birth, so they are obviously out of the picture as to being the ones giving milk or giving birth.
Yes. A cow that is not producing milk is called a dry cow. Dry cows are those that are a result of the weaning process, and are granted a period of rest before giving birth again.
Avoid giving it cows milk, and give it goats milk instead.
Depends on what breed you are referring to. Dairy cows give a lot of milk; beef cows don't.
No because all cows, regardless of type, are capable of giving milk, so long as they have already given birth to a calf (very recently) and are lactating. There are people out there that use their beef cows (yes, BEEF cows) to get their milk from that they use for their own consumption. Milk isn't exclusive to dairy cows only, you know.
You shouldn't milk a goat while it's giving birth. The newborn kid needs that milk to survive.
When they're toddlers.
All cows (mature female bovines) produce milk.
LOL they're the same cows, only thing is that the "colostrum milk cows" are those cows that have just given birth to a new calf. Colostrum flows for 24 to 48 hours, before the milk in their udders "converts" into "real" milk that we drink.
Yes.