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.
"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."
The 3rd person singular reflexive pronoun is "si", not "sé". "sé" is the stressed reflexive personal pronoun, used when the pronoun comes after the verb and after a preposition. Example: Lui pensa solo a sé (= he only thinks about himself)
the verb "vedersi" is reflexive and reflexive verbs must: (1) be conjugated in the "passato prossimo" tense with the auxiliary verb "essere" and (2) agree in number and gender with the subject (in this case, an implicit "lei").