So my alien matriach Queen (see my other posts from much earlier) has a thriving metropolis (which also functions as a pretty grand tourist destination for the whole galaxy), but there's one problem with her ongoing plans: She has many heirs to her own throne... Are there any unforeseen consequences that could result from this palace debacle?
Depends on the style of monarchy and the power structure behind it. An absolute monarchy, along with a lack of good succession laws can result in frequent battles. The roman empire is one such example where a large amount of power, corrupt system and lack of proper succession (along with some amount of historical precedent) resulted in frequent civil wars. Realistically, unless she plans to divide the realm between her heirs, she would elect a single person to take over (unless she just doesn't care, but that typically unlikely). This person would be chosen either on a law or type, or even merit (example: being youngest\oldest). it's hard to say what problems would occur without knowing what type of government is there.
Well, the entire empire is based off a long-term matriachy system, and the queen herself had ruled for over a century of being in power... I was hoping to have a civil discussion about the heirs in themselves for later on, also since this is an alien civilisation I haven't decided the main rules of the palace (as of yet).
So wouldn't the eldest daughter inherit the throne? It's your universe, how is it structured? The British royal family has a strict order of precedence -- read stories about some of the younger members, and they'll usually include a reference to "___ is xth in line for the throne." Or is the successor decided by combat among all the daughters (or all the female heirs) upon the death of the reigning queen? If so, is it a free-for-all, last [wo]man standing kind of melee, or is it a formalized, round robin single- or double-elimination tournament?
Depends on the succession traditions. If your throne is like the British, the eldest of the daughters will inherint, unless she dies all of a sudden (suspicious...). If your realm is more decentralized like the Kingdom of Hungary was, the most influential people might cast their lot with a specific heir. The designated heir can submit and accept the other, or call for a civil war. You could have tanistry, the traditional Gaelic succession where a lesser "vice monarch" is maintained throughout the actual one's tenure. You could even choose the HRE's succession law which calls all major power holders for a moot/election at the death of the monarch.
A monarchy by definition only has one ruler. How can all of these princesses all be the heir to the throne? It simply doesn't make sense.
I was going to have a "trial by elimination" competition format (similar to most traditional fairytale formats, ie The twelve swan princesses), but my story was still in the drafting stages for now... I also didn't know that there were so many monarchies in the world either. Can someone please explain to me the difference between a tanistry and a matriarchy?
Not necessarily. The Roman Empire after Diocletian had four emperors. The Empire ended up fragmenting into the Western and Eastern (Byzantine) Roman empires. The Chinese and Japanese empires largely allowed the emperor (or influential people in court) to designate a successor, so all the princes were vying for their father's favour, and there were a LOT of princes, given that the Emperor had many concubines. That could lead to murder, amongst other things. And look at what happened to Alexander's empire - it split up into several smaller kingdoms, which is what tends to happen when a lot of people claim the same throne.