The joke about Princess Maribel getting plastic surgery and saying she has a "new voice to go with the new face" is to cover the fact that the show switched actresses from Hatty Preston to Jerry-Jane Pears between season 1 and season 2.
The royal tradition of taking a member of parliament (MP) "hostage" is a real one in the United Kingdom. Each year, the State Opening of Parliament ceremony is held in the House of Lords to officially begin each session of Parliament. At this ceremony, the reigning monarch reads a statement (referred to as "The Queen's/King's Speech") that outlines the government's plans for the upcoming parliamentary year.
Before the monarch arrives at the State Opening of Parliament, the Royal Household symbolically take an MP as a "hostage" in exchange for the monarch's safe return. The "hostage" (usually a Government whip) is taken to Buckingham Palace for the duration of the ceremony and entertained by Palace staff.