The three main points in the discussion were:
1. Does the Grand Council in Ebonheart only have a vote in things that concern the whole of Morrowind?
2. Is the Hlaalu noble who replaced the Indoril High Councilor after the war with Tiber Septim Vedam Dren?
3. The UESP article says that Vedam Dren is married to Katariah Dren. Is this correct?
My answer is no, to all three questions.
1. There seem to be two Grand Councils mentioned in the lore.
A. A council that decides in matters concerning the whole province:
Three of Nerevar's associates among the Orthodox Houses, Vivec, Almalexia, and Sotha Sil, succeeded to control of the re-created First Council, re-named the Grand Council of Morrowind, and went on to be come the god-kings and immortal rulers of Morrowind known as the Tribunal, or Almsivi.
Nerevar was killed in the battle, and his ring lost, but Nerevar's alliance survives in Morrowind's ruling political institution, the Grand Council.
In First Era barbaric Dunmer culture, settled Dunmer clans (the Great Houses) and nomadic Dunmer tribes (like the Ashlanders) were roughly equal in numbers and wealth. Under the civilized peace of the Grand Council, and with the strong central authority of the Temple, the economic and military power of the settled Dunmer quickly outstripped that of the nomadic Dunmer.
Actions such as this have led many to label King Helseth as the latest in the lineage of Imperial figureheads, though some of his other actions would cast doubt on this pronouncement. Helseth's reformation of the Grand Council, which includes the heads of all the Great Houses, was seen by some as a return to more traditional Dunmer ways.
B. The Grand council in Castle Ebonheart, overseen by Vedam Dren.
Vvardenfell District's Grand Council, presided over by the sovereign Lord Vedam Dren, Duke of Ebonheart and Vvardenfell, is dominated by five interest groups: the three Great Houses, the Temple, and the Imperial colonists. The Temple and House Redoran are champions of ancient Dunmer customs and privileges, and uncompromising and intolerant worshippers of the native religion call the Tribunal Temple, which venerates three immortal god-kings -- Lord Vivec, Lord Sotha Sil, and Lady Almalexia.
Castle Ebonheart is the seat of Imperial authority on Vvardenfell. Here Duke Vedam Dren, Duke of Ebonheart, and the Vvardenfell Grand Council determine law and policy for the Vvardenfell administrative district. The Imperial cult shrine here serves the Duke, his retainers, and the castle's garrisons, and is also an administrative center for the Imperial cult presence on Vvardenfell.
Duke Vedam Dren, Duke of Ebonheart, is head of the Grand Council and Uriel VII's representative on Vvardenfell.
2. Nothing is known about who replaced the Indoril High Councilor. The only thing we know is that it was a Hlaalu.
3. Same. No reference found to a Katariah Dren. The only Katariah known is the one who married Mad Pelagius. And although the Wolf Queen Series of books states that she was the Duchess of Vvardenfel, there is no known link between her and Vedam Dren.