Translation:She sees hospitals, not department stores.
The translation could also be 'He sees hospitals, not department stores.' Correct?The gender is not specified but implied and ambiguous, right?
A bit late, since it's already accepted now, but: yes, that's also correct. :)
How is the gender recognised here? How would I know if this was first person talking?
You can't tell the gender from the hungarian sentence, it could be either he or she. But you can tell it's third person because it's lát and not látok or some other conjugation.
How should I know that translates to "She sees..."? I thought it said "I see..."
The verb conjugation. Lát is a 3rd-person singular form, so it can translate as "he sees", "she sees", or "it sees" (or even a formal "you see"). The 1st-person conjugation, "I see", would be látok.