When I look the conjugation table for "vedere" up online it always states that you conjugate it using "avere" and not "essere." For example:
Also nothing is mentioned about using a feminine form of "visto." Note that About.com does in fact mention when you can use the feminine form, as in the case of "venire":
But in this case it doesn't mention it. Why the inconsistency here?
Because this is actually the reflexive verb vedersi, not vedere.
I believe the two verbs are distinct, and used in different circumstances. vedersi is used when reflexive, and it takes essere, like this sentence. But, if the verb is transitive, e.g. takes an object, then use avere .. lei ha visto il suo cane.
You always use essere when a verb is reflexive, so although vedere itself uses avere, vedersi uses essere because it's reflexive
Because, if the subject is masculine, the sentence would be "si è visto allo specchio" (he saw himself in the mirror).
"to look at oneself" would be "guardarsi".
"She has looked at herself in the mirror." = "Si è guardata allo specchio."
"She looked at herself in the mirror" would usually be in the past absolute tense (or "passato remoto", which we haven't covered yet): "Si guardò allo specchio."
Why the correct solution is ''She's seen herself at the mirror.''? Can't it be ''She seen herself at the mirror.''?
"She seen herself at the mirror" is grammatically incorrect in English. "She's seen" is basically a contraction of "she has seen," which is the past perfect form indicating something started in the past and has continued up to the present. "She seen" doesn't exist.
"vista" is the feminine past participle of the verb vedere. (visto would be the masculine) The verb is being used reflexively, that is both the subject and the object of the sentence is the same. (She saw herself) so the reflexive pronoun "si" (himself / herself / itself / yourself / themselves) comes at the beginning. Literally it is "Herself she is seeing in the mirror" and the only way you know this refers to a female is by the ending of the past participle. Hope this helps :)