So... what can magic do in this setting? How powerful is it?
very fantasy kitchen sink. Alchemists creating horrors using Not!genetic engineering which leans closer to science. Elves tossing sparkles and sunbeams into cauldrons and creating love potions. Various flavours of dragons are flying (or swimming, or burrowing) around.
Luminaire, the kingdom of light. Didn't get that the name by accident. First queen was predominately a light mage, and the grand ritual means every queen after her, and any loyal subject who the queen loans power out to, it leans towards manifesting itself as light magic. Often glowing barriers, or flashes or beams of light used instinctually with a thought.
Almost everyone has at least 'some' basic magic. lightning a small fire, warming a cup of tea. often someone develops their own small trick which can be as varied as reading the thoughts of your pets to healing minor injuries to stunning someone with a blast of lightning. But having more than half a dozen small spells is rare, and most people often don't know more than the basic three in luminaire. That is, boiling water, creating a small witchlight to see at night, and channeling a small amount of magic into an object or person to power an enchantment or will them power for a spell.
The title of 'mage' however. refers to those with an actual understanding of magic, who can shape and create more spells, based upon more than simple instinct.
mages are arranged into tiers. You've got your basic hedge mages. Think a village witch or healer, largely self taught or with spells taught by a family member. They'll have at least one spell for self protection, even if they can only use it in emergencies, such as a fireball spell that leaves them drained for the rest of the day.
Beyond that is a mage. There's no standard here since every mage is different, but this is where you get recognised as the classical mage. Able to cast multiple combat spells per day, and earn money as mercenaries. Even at this low level, they're Eagerly snapped up by armies as they can often protect small groups of allies from hostile magic, and combat enemy mages.
Above that is Mage Knights. to most, they appear to be unstoppable forces of destruction. They may or may not specialise in long range spellcasting. But they're powerful enough to be noted, many become famous folk heroes, and almost all are accorded some sort of minor noble status.
More powerful are battlemages. As the name implies, they have a heavy focus on combat. And just one can decide the course of a battle. Smaller countries are lucky to have just one of these. To reach this ranking you need to have a vast wealth of knowledge and be among some of the most powerful mages on the continent.
The last two mage titles are honorifics. Warmage. And Archmage. One Can sway the course of wars. The other, it's no exaggeration to say that Archmages change the course of history. The First queen of Luminaire, for example, turned a small kingdom of farmers with a talent for sun spells into the continental great power.
the world lives and runs on magic. Everyone has some. Those with a lot rule the world. Powerful magic bloodlines rule as royalty or nobility, in other nations councils of mages rule. Almost everyone has a court mage or some mages in their army. And an army without magical protection is practically helpless. Mages are the artillery, tanks and sometimes even airforce of the military. Enchantments exist, great and small. From stoves with a fire spell that you either channel magic into or use some other source of power. To winter clothes enspelled to keep the wearer warm.
Animals and even plants are magical. Lizards with regenerative tails and limbs to size-changing wolves to dragons or griffons.
If you can imagine it, chances are, someone, somewhere can do it. Or if no-one can, that's only because no-one has figured out how to do so yet. The world is... largely operating on standard medieval tech level with some magi-tech.
Various kinds of necromancy exist. A lot of the more powerful applications of death magic are banned in most countries. But the practice persists as it's often seen as a quick (if dangerous) route to power.
So the Queen is still receiving magic from the peasants via the old ritual? And the taxed magic power is redistributed by the Queen to the nobles?
Are there non-magical nobility, or non-noble magical lieutenants? Are all nobility expected to be mages or are there court mages that can help if someone without talent inherits? Or is the job by appointment only without any family inheritance?
So long as they're loyal to the queen yes. Technically the Princess hasn't been crowned yet, but yes, she receives power as the queen already.
Redistributed to the nobles if/when they pledge their loyalty to her, some kept for herself. Those who join the royal army, even if previously magically weak, often see a small increase to their power. One thing to note is the queen isn't in complete control of where she sends the power. She can't decide to send a specific amount to a specific person. A problem with it being ritual magic working by emotions such as loyalty and trust, is it operates mostly on her sub-conscious. Influenced slightly by her waking mind, so she can choose to gift a small amount of power to someone she appoints as a general or such. But there are limits and safeties built into the spell. As a rule of thumb, she can't make anyone stronger than herself, and this is a spell that operates on emotion. Not logic.
Yes. Rarely. Non-magical nobility in other kingdoms almost always employ a mage of their own, and frequently nobles lacking magic attempt to marry mages into the family. This is less a concern in Luminaire as those nobles without enough strength to be classed as mages can be empowered by the bond.
Non-noble magical lieutenants. Yes. A number of the royal bodyguard have or develop magic and are trusted to carry out her will.
Generally yes in Luminaire, the nobility are expected to be mages. But also yes, sometimes a noble without any magic is allowed to inherit the lordship of a house. At least if any magic wielding family members don't contest it. It's customary for a non-mage noble to step down in favour of younger magical siblings, and the crown can enforce such in emergencies. But there are some families which prefer not to put their eggs in one basket, and send a younger mage to represent the family in times of war, while the non-mage house head handles the family estates and such.
The queen can appoint and strip noble titles or military ranks or governerships. But generally doesn't do that without good reason.