"Whenever they see him, he is talking."
Translation:Όποτε αυτοί τον βλέπουν, αυτός μιλάει.
Όποτε τον βλέπουν, αυτός μιλάει is the correct one. Τον is used for direct object "they see him-τον βλέπουν" whereas του for indirect object "they give him an apple-του δίνουν ένα μήλο
Όποτε is whenever, όταν is when. So for the above sentence, the most appropriate translation is όποτε.
You cannot, if the word is on its own. But here it says "αυτοί τον βλέπουν" so it can't be αυτή because it would be "αυτή τον βλέπει"