Learn Spanish (Spain): ¿Todavía trabajas en el hospital?

In Spanish, the preposition en covers "in", "on", and "at". There isn't a separate word for "at" a location, so whether you are physically inside the building or just employed there, you say you work en el hospital.

Can todavía mean both "still" and "yet"?

Yes! In affirmative sentences and positive questions like this one, todavía means "still". If it were used in a negative sentence, like todavía no trabajas, it would translate to "yet" (you do not work yet).

Could I change the word order and put todavía at the end of the question?

Absolutely. Spanish word order is very flexible. You can say ¿Trabajas en el hospital todavía? and it sounds completely natural and means exactly the same thing.

Do I pronounce the letter "h" in hospital?

No, the letter h is always completely silent in Spanish. You pronounce this word like "os-pee-tal", making sure to put the spoken emphasis on the final syllable.