Supernatural is perhaps not the most accurate or comprehensive expression, as
@tampasteve rightly points out, but it’s not wrong. It is effected by God’s power after all.
And yes, it’s Christ’s glorified body. Remember that the Sacrament was instituted on the night when He was betrayed, before being crucified, so the next time His disciples would have celebrated it would be after His resurrection.
Oh, that’s very interesting! Would you say it’s a somewhat casual or modern church?
With respect to the validity of the Sacrament - this is not subject to any thing or quality in the priest, but simply Christ’s word, which does what it says it does. It’s not effective by our power or authority, but by God’s power and authority.