Sigh...after much searching, I could not find the first quotation, except in different versions in other polemical sites (and out of context, as usual). Epistles from Pope St. Gregory are listed here: http://www.newadvent.org/fathers/3602.htm
Here is an epistle from Gregory to Patriarch John of Constantinople. I see similar ideas expressed in it, but not exactly the first quotation you pasted above. http://www.newadvent.org/fathers/360205018.htm
These quotations are worthless without context.
I always found this argument odd, considering Pope St. Gregory was condemning the Patriarch of Constantinople in that letter for assuming the title Ecumenical Patriarch which, Gregory thought, implied that the other bishops were only agents of the one bishop and not bishops themselves (Gregory insists that was the reason why the Popes refused that title when the Council of Chalcedon offered it to them).
It is also odd to me that polemicists simultaneously criticize Pope St. Gregory as one of the first real Popes (meaning, overreaching his authority and building the papal supremacy) while also using out-of-context quotations from him to "prove" that papal supremacy did not exist.
I did find the second quotation (way out of context). It's from a letter to Emperor Mauricius: http://www.newadvent.org/fathers/360205020.htm
I can't help you with the third quotation. Can't find that either. You are quoting from an article which is quoting from a book supposedly quoting from a translation of Gregory. Not easy to find these things.