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I seriously doubt any answer you studiously prepare will be acceptable to this well known "trick" question. It's a set-up, pure and simple. To demonstrate my conclusion, I'll answer the questions posed and then you will see how they are received and their "ad hominem" type sideswipe character will be revealed. Here goes:

What members of your church attended the Council of Nicea to fend off the gnostic and Arian heresies? Which of them put down the pelagius heresy.

The "members" of the church of Jesus Christ, His body, consists of ALL believers and followers of Jesus Christ from all time, so those who counted on Divinely-inspired Holy Scripture to dispute the heretics back then are as much members of the body of Christ as those of us who follow him today. Today's Roman Catholics like to claim they are members of the same church as the early Christians and that ONLY their current church is the same one as established in that first century. This can easily be shown to be in error as there are many doctrines and dogmas that they hold to today that were unheard of in the Apostles' time or that have CHANGED since then.

Where was your church during the Council of Constantinople that settled the matter of the filoque?

See above answer. As a side note, are you implying that the Orthodox Church, which disagrees with the "filique" of the Roman Catholic Church, is not equally as genuine as they are?

Can you identify the members that helped to define the doctrine of the hypostatic union? Which of them was present at both Hippo and Carthage ordering the canon of the New Testament?

See answer to first question. See how easy it is to settle false constructs once one has the actual truth revealed? Where were "our" church members back then? The same place as those who hold to the Biblically revealed Christian faith today.

there are those that claim to be part of the same Church that existed for the first 15 centuries after Christ, but it can easily be shown that they could not possibly be, since they would be able to worship in that Church, just as they don’t worship in that Church today. Justin Martyr explained this very well in his work defending the Faith to the Roman Emperor:

Justin Martyr, Apology, I.66-67, 2nd century:
Communion in the Body and Blood of Christ

It is allowed to no one else to participate in that food which we call Eucharist except the one who believes that the things taught by us are true, who has been cleansed in the washing unto rebirth and the forgiveness of sins and who is living according to the way Christ handed on to us. For we do not take these things as ordinary bread or ordinary drink. Just as our Savior Jesus Christ was made flesh by the word of God and took on flesh and blood for our salvation, so also were we taught that the food, for which thanksgiving has been made through the word of prayer instituted by him, and from which our blood and flesh are nourished after the change, is the flesh of that Jesus who was made flesh. Indeed, the Apostles, in the records left by them which are called gospels, handed on that it was commanded to them in this manner: Jesus, having taken bread and given thanks said, ``Do this in memory of me, this is my body.’’ Likewise, having taken the cup and given thanks, he said, ``This is my blood’’, and he gave it to them alone

so unless one believed in baptismal regeneration and the Eucharist is the Body of Christ, that Church would consider anyone rejecting these doctrines as they thought of the Gnostics, a heretic.