Is saying "wa Lillahi" (by Allah) considered an expiation, and is she considered an unbeliever if she swore in a state of anger by saying "wa Allahi al-Adhim, innī mā asmaḥuhu" (by Allah the Almighty, I will not forgive him), and then regretted it?

If one swears by Allah Almighty willingly, then expiation for an oath is due upon him if he breaks it. Anger does not prevent the oath from taking effect as long as the swearer is aware of what he is saying. If the oath was to abandon a recommended act, then it is recommended to break it and offer expiation for the oath, based on the Prophet's (peace and blessings be upon him) saying: "If you swear an oath, and then you see that something else is better than it, then offer expiation for your oath and do that which is better." It is disliked to uphold an oath if it was sworn to commit a disliked act or to abandon a recommended one.