Yes, they have a high quality meat.
Limousin cattle are beef cattle.
Dairy
That all depends on the breed. Are you asking about a dairy cow or a beef cow, and what breed of dairy or beef cow?
Nothing wrong with that. Dairy cows are slaughtered for beef as culls anyway, so it's no big deal if you slaughter a dairy cow and turn her into ground beef.
No. The biggest type of bovine is typically the beef cow. There are beef cows around that weight more than a big dairy cow, and that can be upwards of 2000 lbs or more.
Yes.
Primarily for beef production. Historically, Limousins were also used for draft and even dairy production.
No. She is a dairy cow, one that is used to primarily produce milk.
Beef and Dairy products.
The average beef cow will live until they are about 15 years of age or longer, however, if they are being used for beef production they will live until they are about 1-2 years of age.
No. A Hereford cow will only give birth to a Hereford-Limousin cross calf if bred to a Limousin bull. Only a Limousin cow can give birth to a Limousin calf--IF she's bred to a Limousin bull. Just like a Hereford cow can only give birth to a Hereford calf if bred to a Hereford bull. Otherwise, she too (referring to the Limousin cow) can give birth to Hereford-Limousin-cross calf if bred to a Hereford bull.
For beef and dairy cows, lactation period begins immediately after a calf is born. For beef cows, the lactation period ends when their calves are weaned off of them. For a dairy cow, the lactation period ends when she is not longer being milked and allowed to dry up so that she can focus on putting energy into growing the calf inside her. The dry period for a dairy cow is shorter than a beef cow's: two months for a dairy cow, and four to five months for a beef cow.
Limousin cattle are a beef breed, not a dairy breed of cattle. So in other words, no not really. They have a milking ability that is matched to that of Angus, which is not nearly as good as Holstein or Jersey.