Well...no. Your conclusion was correct but your assertion was incorrect

Well yes but also no. Although dairy cows are not mainly used for meat they still end up that way at the end. And you do not want old tough meat. So it is not just because of the industry but also to be profitable

Funny enough cows pregnancy last for about 9 months. Followed by aboht 10 months to a year kf milking period and then the dry period. How many cycles deoends on how healthy the cow is but they should last for about 10 years before they are too old.

Veterinary technician here. Short answer: No they do not. Long answer. When a cow gets a calf she produces milk. The more they milk her the longer she sill produce milk as her body thinks its feeding a calf. The production of milk slowly reduces over time and farms need to calculate this in order to be profitable. Once it is not profitable anymore they stop and wait until she recovers and is ready for another calf.