It's possible but I think it means something slightly different.
- Hat sie sich im Spiegel gesehen? = Did she see her reflection in the mirror? Or is she a vampire and she saw nothing at all? (Basically: did the action "she saw herself in the mirror" happen?)
- Hat sie sich selbst im Spiegel gesehen? = Did she see herself in the mirror? Or was it a magic mirror and she saw someone else instead? (Basically: Is the person she saw "herself"?)
Because the verb hat is third person singular (he, she, it), so sie must mean "she" here.
If it had been "they", then sie would take the verb form haben.
Also, "they looked themselves" sounds odd to me in English -- "they saw themselves" or "they looked at themselves" would sound better to me (and given that the German uses sehen rather than sich ansehen, I would prefer "saw").
Not necessarily. What about wing/rear-view mirrors in a car etc? Also, you can look at other people or things mirrors; oneself is just the default. Admittedly the at oneself is unnecessary in many cases due to context, but that doesn't mean it's unnecessary in isolation, nor that it shouldn't be included even if the context allows it to be left out.
Has she seen herself in the mirror - is not accepted.
That's one of the accepted translations.
Did you, perhaps, have a listening exercise rather than a translation exercise?
Please post a link to an uploaded screenshot showing that sentence being rejected (showing the question, your answer, and the error message) -- it will help to understand what might have happened.