"The teacher eats an orange."
Translation:Le professeur mange une orange.
"enseignante" is accepted provided the rest of your translation is correct as well.
"le" and "la" have to elide in front of a word starting with a vowel sound:
- l'enseignant / l'enseignante
Oui, but context would tell that the teacher is a "she" : "madame le professeur XX" or "la femme professeur" or "le professeur femme", for example; otherwise, a larger context will most probably use "elle" at some point.