1)IMHO, the use of the Latin "Co-Redemptrix" not only accurately describes the concept but is also a "red flag" that indicates to the reader that it may not mean what its English counterpart would allude. In second place would be "Co-Redemptoress" as used in the title of the earlier article. This at least, alludes to a subordinate status, but the prefix can be misleading. Is it Latin or is it English. Third place, which should never be used, IMHO, is "Co-Redeemer." It is way too English. Sounds like equal to the Redeemer, which is not what Co-Redemptrix even remotely means.
2)There is no value in mis-communicating, that is why the Latin is used, so that there is a precise definition.
3)No. As in # 2, to give a precise definition to avoid confusion.
If all this means is "submission" Why not simply call her "an obedient and key servant of God of extraordinary faith?"
Three reasons. 1)What you said above is a mouthful. :) We human beings like to say and write our thoughts in the simplest and shortest form possible, because it is practical. We don't say, for instance, "I need two acetylsalicylic acid tablets," rather we say, "I need two aspirin." So we come up with words that shorten a longer definition.
2) Your definition above, though an accurate description of Mary, is rather broad in its meaning. Co-Redemptrix describes one facet of Mary, just as Co-Mediatrix describes another facet of Mary, and so on. As an example, take my screen name. It describes two facets about me, that I am of the male gender and I "play" the pipeorgan, but it doesn't inform anyone what kind of work I do, the color of my hair, etc.
3.) Your definition could be used to describe any "good and faithful servant." [I assume you are describing me.:)] Seriously though, could this not apply to say Billy Graham? Is he not obedient to God, have an extraordinary faith and isn't he a key servant of God?
So, IMHO, it is necessary to have precise terms to avoid, any resulting confusion. The key with precise terms, as with any word, is knowing the proper definition.
OK, so why am I so confused now?..... Don't answer that. Lol (*g*)