This question has actually been answered in several separate questions, all in as much detail as could be made to give you as much information as possible. Also check out the related links.
That all depends on how big your cow herd is and how many bulls you have to breed them with.
No. A cow or heifer in heat will stay with the herd, or rather, the herd will stick with her.
Because it isn't a cow-herd
A herd of cows or, if they're not fully matured, heifers.
Yes.
herd
A harem.
No, but the breed you may be thinking of would possibly be the Montbéliard breed, which is similar in spelling. Check out the link below.
Cutting is removing a single cow, or group of cows, from the main herd. A good cutting horse can allow the cowboy to isolate the cow, whether it is to brand it, check it for injuries or move it into a location for sale.
It depends on the horse. There are some horses that are breed for herding cattle. People often use them for 4-H and do roping because the horse tends to want to chase the cow or herd them. These horses are called cutting horses.
A herd.
A herd of cows.