Here I will be talking about many things of wizarding world. Judicial and Legislative body, Family Magic, Ley Lines, Nobility etc.

Let's start with Ley Lines.

Ley Lines are like natural rivers of magic flowing all over the world. Natural magic, that is the raw magic of the world is very strong here. Many strong and rich wizarding families build their homes above these lines as this help grow their natural reserves and can power very strong wards easily. You can live in other places and have wards charged on natural magic, but ley lines can charge highly mana consuming wards for 100 of years. Many reserves of magical animals and their natural habitats are also located on these lines.

The point where 2 or more ley lines meet are very rare but is very magically potent. Hogwarts is built on one such confluence where 7 ley lines meet. 

Let's talk about the government structure.

The executive body is the Ministry of Magic. It was created in a bid to shift from monarchy to constitutional monarchy and reduce the fights between different houses. No one knows where it started but later it was copied in the whole world. 

The legislative body is the Wizengamot. In this the nobility of the country, department and sub-department heads and Order of Merlin (or its equal in different countries) recipient can vote. The Secretaries of these heads can bring new bills for discussion, but they can neither vote nor discuss about any other bill.

Sub-Departments - 1 vote

Departments - 3 vote

Order of Merlin - 1, 2, 3 vote depending on the rank of award.

Minister, Chief Warlock - 5 vote

Nobility -

Nobility in Europe is divided into ranks like the House of Lords while in other country they follow their own designation.

Knight - 1 vote

Baron - 3 vote

Viscount - 5 vote

Count - 10 vote

Earl - 15 vote

Marquis - 20 vote

Duke - 30 vote

Arch-Duke - 40 vote

King - 50 vote

Judiciary is like normal world but in some cases Wizengamot tends to work in the place of judge.

Family Magic

It can be divided into 3 parts.

Affinity

Magical Beast

Blessing

Affinity is a part of field of magic where due to constant practice for generation and using a ritual noble family have bound it to their bloodline. They are of two types major and minor in higher ranking family and one in lower ranking family. Their strength and benefits may vary from the rank of nobility rank.

For ex- A Knights major affinity is battle transfiguration and an Earl have same as a minor affinity, and they duel of purely transfiguration even than there are chances that Earl may defeat the Knight.

Anyone of higher ranking than Knight can create a new Knightly House but either the House should previously own a Keep, or they have to provide them with one for them to be recognized in Wizengamot. Previously you had to seek the permission of King but in Wizarding Britain the line of King is long dead so you can circumvent this rule.

Magical Beast

As a magical beast grow stronger, they gain sentience. These sentient creatures are like nukes. Starting from a few creatures now almost every beast has made a pact with a powerful family for support in war in exchange of sanctuary for their race and species.

Lower ranking family, generally Knight and Baron, don't have a beast of their own, that's why they decide to become vassals of higher-ranking family who give them a beast that is sub-servient to their own beast.

Blessing

Old wizarding family through rituals have gained the favor of gods, demons, angel etc. for their family. You provide them with sacrifice and rituals which increases their strength and help in strengthening their domain and in exchange they give your House their blessing according to their domain.

For Ex - A god of knowledge will ask you to make libraries and school and in exchange will give you blessing that increases your intelligence, wisdom and learning speed.

Or a god of war will ask you to bring old war relics back into use and give you their blessing which increase your physical attributes and martial skills.

Any family with knowledge of appropriate rituals can invoke a god or such deity, but you have to complete their task which may be very hard, to gain their favor. Generally lower ranking family just invoke the same god as their lord.

Nobility

Nobility rank I have already explained but why are these nobilities so important. That's because these nobles are allowed to keep their own private army but need to lend their support in wars.

Ministry couldn't do anything against it as the ministry have all their power because of them and they could easily dissolve ministry. That's why ministry has to keep many of the old laws like law of Casus Belli in which a House can declare war on another House for a period of time. Many Houses get extinct in these kinds of things and all the lands and property of both sides are fair game and whoever wins it gets to keep it.

But that doesn't mean you will gain their Family Magic of you wipe out the House or there vote in Wizengamot. You may raise the rank of a House by giving them these properties and give them the name of the House you wipe but you can't yourself keep the Magic and Votes.

The spells in the family grimoire become just some new spells which may be strong but without family magic will be hard to learn.

That's why lords prefer to capture the daughter and have your son, grandson or whatever become the lord of the House.

Now if you want to increase your nobility rank, you need to have a suitable as there are benchmarks about the stronghold you need to govern to be that ranks noble.

Like you need a small keep for a Knight.

A big keep for Baron.

A small castle fortress on a small ley line for Viscount.

A big castle fortress or a castle and a fortress on a small ley line for Count.

A castle and a fortress along with a villa for showoff is the norm on a major ley line for a Earl.

And so on

Along with that you need enough wealth and income. Many houses above Viscount also keep a 'Tower' where they conduct research and make stuff for sales. It is actually tower in name only, actually it is their industrial ground.

Nowadays, it is next to impossible to rise above Viscount.

Also, you can make any house of lower rank your vassal but a house of similiar rank can only be your Ally.

Nobles Army Size

Knight - 100 men

Baron - 250 men

Viscount - 500 men

Count - 1,000 men

Earl - 5,000 men

Marquis - 10,000 men

Duke - 25,000 men

Arch-Duke - 50,000 men

King - As big as he likes but generally 100,000 men

Previously it was managed by the King that they follow cap on army size but due to there being no King in Britain and Ministry lack of power here this rule can only be implemented through fear of retaliation from others.

That's also the reason why lords are rarely sentenced. Ministry can't send a whole army to their doorsteps to arrest them now can they.

Lestrange were captured in a stroke of luck without their army and only 4 of them and that too red handed and they were the last of their house so no retaliation after all an army rarely works without a leader.

The men in the army gain some affinity of their lord so they can use major spells that are only effective when cast by a large group.