The main campus of California State University -- Fresno is 388 acres.

Yes. Fresno State is a large public university in the California State University system.

Cal State Fresno is a state university. It is not private. The term "university" has no bearing on whether the school is public or private. Schools in California that begin with California State or University of California are public state schools (e.g., UC Irvine, Cal State Long Beach, etc.)

The most popular Fresno would be in California, though there are towns of the same name in both Ohio and Texas

If Fresno State University is in California, you can't become a veterinarian there. The two colleges of veterinary medicine in California are UC-Davis and Western University.