Point 1. I created the Ancient Greek category for this work the day after it was posted (in accordance with the language as given by the poster) . As for the Kyrie eleison, the Divine Music Project refers to the language of the Divine Liturgy as being simply Greek. On a similar point, we have almost no clear idea how Latin was originally rendered, but we still call it Latin, not Ancient Latin (and is there such a thing as Modern Latin?). My feeling about the Kyrie eleison is that it is pretty much universally considered Greek (even though it has ancient origins), and it has remained unchanged from ancient times to modern times (as far as I know). On the other hand, there are definite differences between Ancient and Modern Greek, just as there are with Old, Middle, and Modern English. And a phrase such as "Thy kingdom come, Thy will be done" from the Lord's Prayer is still considered English (it is not Middle or Old English), even though many branches of English/American Christianity render it differently (such as "Your kingdom..."). The Ancient Greek category is suitable for texts reliably identifiable as ancient and not the same as in modern usage (at least that's what I thought I was doing). If the "Pater Hämon" is really the normative Greek version of the Lord's Prayer in use today, then it's category should be changed from Ancient Greek to Greek. But for this, I think an expert would have to weigh in on the issue.
Point 2. Wikipedia is often wrong (just as we are), especially on musical matters, and I'll try and track down the Wikipedia reference and change it (if it hasn't been changed already). Note: I found the reference at Wikipedia and have now corrected it.