Edit: Changed title to be more accurate.
Also here is the summary from Wikipedia on what Post-scarcity means:
Post-scarcity is a theoretical economic situation in which most goods can be produced in great abundance with minimal human labor needed, so that they become available to all very cheaply or even freely. Post-scarcity does not mean that scarcity has been eliminated for all goods and services but that all people can easily have their basic survival needs met along with some significant proportion of their desires for goods and services. Writers on the topic often emphasize that some commodities will remain scarce in a post-scarcity society.
Sort of. Monarchism is more about respecting a family’s right to rule, than a claim on economics, though usually Feudalism goes hand in hand historically. The British parliamentary system with a vestigial Monarchy is an exception, not the rule.