Is गाजर both sing & plur, and therefore this is more likely to read: She eats carrots? Would एक गाजर be needed if it was only one carrot?
No, I think it became she because it said खाती which is the female version of the verb. If it said Khatha it would have been He.
"vah" is the actual pronunciation of वह. Unlike the pronunciation of वहां which is "vahaan" with a nasal "n" after the long "a" To pronounce वह "vo" is rather colloquial. (https://www.duolingo.com/skill/hi/Basics-1/tips-and-notes)