Yikes, let’s at least get history straight before we try to answer questions…
James I of England (James VI of Scotland) was a Stuart. The Stuarts had ruled Scotland since 1371, when Robert II (Stuart), son of Walter Steward and Marjory Bruce, ascended to the throne. The name was spelled Stewart, from Steward, until Mary Stuart, who was quite the Francophile, changed the spelling. The monarchs of Scotland were, in order, Robert II, Robert III, James I, James II, James III, James IV, James V, and Mary. James IV was married to Margaret Tudor, daughter of Henry VII of England.
Mary Stuart abdicated the Scots throne in 1561, and her son, James VI was made king. When his first cousin twice-removed Elizabeth I of England died, he was accepted as king of England (by act of Parliament if I am remembering correctly, as well as by law of primogeniture.
James I (VI) was followed by Charles I, Charles II, his brother James II (VII), Mary II (who was also Mary II in Scotland) who was James’ daughter, and Anne (no designation, there having been only one Anne who was queen regnant), another daughter of James. At that point, Anne having failed to produce an heir who managed to outlive her, the direct Stuart ruling line ended (there were, of course, the son and grandson of James, known as the Old Pretender and the Young Pretender (also known as Bonnie Prince Charlie).
After James I (VI) became King of England (retaining his title as King of Scots), he ruled as the king of both countries. This was not new, particularly; dual monarchies had existed before in Europe and Henry VI had theoretically been King of England and King of France (he was the grandson of King Charles VI; his claim was disputed by his uncle, who became, with the help of Jeanne d’Arc, Charles VII despite the Treaty of Troyes, in which the French had agreed to have the succession go through Charles VI’s daughter Catherine, who had married Henry V of England). The kingdoms of Scotland and England were not fused until the Act of Union (1707), when the parliaments of both countries were united, and the country became the Kingdom of Great Britain. Thus, as you can see, until 1707, the nomenclature wouldn’t have to have changed. (Someone with better understanding than I can look up and address what the Scots called William III of England)
The first king/queen whose name would have forced the United Kingdom to decide what to do about nomenclature was William IV (ascended 1830). Someone with more understanding than I can provide information about whether the issue was addressed by Act of Parliament (for all I know it is addressed in the Act of Union (1707). I’ll poke about to see if I can find the answer.
As for queens who were not rulers, their names do not figure into the numbering scheme, just as prince consort names do not. There were numerous Marys, Elizabeths, Isabelles, etc. who were queen in England; the fact that the English didn’t ever see fit to come up with a new term for a ruling queen doesn’t affect this issue.
Information used herein came from several sources, including Compton’s Online Encyclopedia (Compton’s Online) and A History of Scotland, J. D. Mackie.