Short answers, pulled from the story.
The name Stuart derives from the office of High Steward of Scotland, first held by Walter fitz Alan around 1150. The spelling Stewart was standard until Mary, Queen of Scots adopted the French spelling Stuart during her upbringing in France.
Robert II was the first Stewart monarch of Scotland, inheriting the throne in 1371 after his uncle David II died without children. His mother was Marjorie Bruce, daughter of Robert the Bruce, and his father was Walter Stewart, the sixth High Steward of Scotland.
In 1503, James IV of Scotland married Margaret Tudor, daughter of Henry VII of England. When Elizabeth I of England died without heirs in 1603, James IV's great-grandson James VI of Scotland inherited the English and Irish thrones as James I, uniting the crowns in a personal union.
James VII and II was deposed by Parliament in 1689 after converting to Catholicism and fathering a son in 1688 who was to be raised as a Roman Catholic. Parliament replaced him with his Protestant daughters Mary II and, later, Anne.
The Royal House of Stuart became extinct in the direct line with the death of Cardinal Henry Benedict Stuart in 1807. He was the brother of Charles Edward Stuart and the last direct descendant of James VII and II.
Franz, Duke of Bavaria, of the House of Wittelsbach, is the current Jacobite heir to the historical Stuart claims. He is a distant cousin connected through the dynastic network that developed after the direct Stuart male line ended in the early 19th century.