As regards ordination and consecration, Katzpur, I think LoTrabador was correct, it is a separate, though linked, question from authority.
I said, in ordination, the priest is ontologically conformed to Christ so that he shares in His priesthood in a way that is unique from lay members of the Church (who all share in the general priesthood, or the priesthood of all believers).
A priest who breaks communion with the Church still retains the faculties to celebrate the Holy Sacrifice of the Mass, or any of the sacraments. However, in doing so, he must preserve the proper form, intent and matter of the sacrament. Secondly, while the Church acknowledges that all who are ordained by her posess valid holy orders, any such sacraments performed outside of ecclesial unity are valid but illict. That is, they are performed without the proper authority to do so.
Why is this all so? This is because, in the New Covenant, the sacrifices of the Temple have been abolished and surpassed by the "once and for all" sacrifice of Jesus Christ Himself- both the victim and the High Priest of His offering.
The priesthood of the New Covenant is therefore unable to offer anything new, anything other than what Christ did once and for all. Thus the priest is ontologically- at the level of his being- incorporated into the priesthood of Christ. The priest is then co-joined with Christ and becomes a participant in the offering of the sacrifice of the New Covenant: the Paschal Victim, Jesus Christ.
The Holy Mass is the once-and-for-all offering of the Cross in 1st century Israel extended and brought through time and space to God's People here and now.
In the Holy Mass, at the hands of the priest, the self-same sacrifice of the Cross is "renewed", or in other words, is made present to us in this given moment so that we too might become participants.
The priest, working in persona Christi, that is, "in the person of Christ", makes the sacrifice of Christ's Body and Blood. The lay participants bring themselves to this Sacrifice, join themselves to it as members of Christ's Body, and incorporate themselves into the Living Sacrifice of Christ to the Father. In this way, the Holy Mass constantly renews the Christian life, as we constantly return to the source of our salvation.
It is also because the priest, having been ontologically conformed to Christ the Priest and therefore working "in the person of Christ", must be male, as Christ was ontologically a male.
Any other Catholics reading this, feel free to correct me if I have misunderstood something.