Kingdom of Poland

Kingdom of Poland is a unique country. One of the youngest ones and one of the newest participants of the Great War. It was created as a de facto (but not de iure) satellite government of the German Empire. Trying to ride on this particular horse ended pretty bad for the kaiser, however.
Kingdom of Poland managed to shake off all manners of political dependence on the German Empire following the Ludendorff's coup, when the sudden revolution almost crippled the country. And to Austro-Hungarian Empire following the Todesmarsch. It remains a part of the Central Powers, obviously. But it also has its own ambitions.
According to some, even if Kingdom of Poland helps the Kaiserreich win the war (or at least survive) it will only do that to become kaiser's worst nightmare in the following years. For now, however, the two countries are allies - and can't stop being allies, as that would spell doom for both of them.

Structure

Kingdom of Poland is officially a constitutional monarchy, with Józef Piłsudski being its regent. The part about searching for a monarch is postponed currently and left for the times after the war. For now it is in a state of perpetual regency, similar to Kingdom of Finland and the Belarus and Ruthenia Grand Dukedoms.
Piłsudski himself is far from being a monarchist himself, and the future of the monarchy in Poland is uncertain. For now, remaining a monarchy is useful from political point of view and the Kingdom's association with monarchist central Powers. In the future, things might change. Some opt for the full democracy. Others suggest a monarchy when king rules but not governs, making him nothing else than a symbol.
There is also a theory that Piłsudski treats the crown as a bargain chip, that might be used to bring Poland closer to the Austro-Hungarian Empire, to counter the German Empire post-war revanchism. If that's a thing, there is a big chance that some Habsburg or a closely associated aristocrat might end up a king after the war ends.
Right beneath the regent himself is the Regency Council of the Kingdom of Poland. It underwent major reorganization at the hands of Piłsudski following the Ludendorff's coup, when German control over the Kingdom faded away. It is now an advisory (sort of) group of most influential people in Poland. It can be considered a platform that connects all major political movements in the country, from Polish Socialist Party to National Democracy.
It creates the government together with the regent. It is officially accepted after the parliament accepts the proposed cabinet.
Beneath it is a parliament, composed of two chambers - lower, the Sejm, and higher, the Senate. Sejm is composed of elected representatives of the entire nation. Senate is composed of ministers, high ranked officials, most important generals and bishops. King is able to add people to it, in his absence this right belongs to the regent.

Public Agenda

Kingdom of Poland - and the regent himself - has a single, chief political agenda. Survival. The country regained independence after more than a century of being partitioned between its neighbours... that are now tettering on the edge of abyss.
It needs the German Empire and Austro-Hungarian Empire to survive. But they also need it to survive. Kaiser could do nothing when Kingdom seized Greater Poland and (partially) Silesia. He could do nothing when Poland annexed the Ober-Ost and created two satellite Grand Dukedoms that respond to it, and not to Empire.
Poland has to make sure that its allies survive... and Axis is defeated. While simultaneously gaining enough ground and power (military, industrial and political) for the Kaiserreich - even in its full power, easily capable of outnumbering Polish Army and having much more powerful industry - to be unable to lay a finger on it.
It is a desperate bet. But until now, Poland seems to succeed.

History

Poland was partitioned between Russia, Germany and Austria in late XVIII century, ceasing to be an independent political entity for more than a century. It also was a contributing factor to the eventual start of a Great War, as the collapse of the Polish-Lithuanian Commonwealth left a power vacuum in the region, elevating power of Germany and Russia, forever ending the ancient balance of power.
With several uprises squashed, the polish independence movement changed its tactics to improving political and industrial strength of former Poland lands (while stimulating the polish culture) in preparation for a war between the three partitioners. Which finally came, in the form of the Great War.
When the war started, two main political views emerged. Józef Piłsudski saw hope of independence in supporting the Central Powers. Roman Dmowski, in the same time, supported Russia (and, by extrension, Entente).
Piłsudski's idea culminated (or so it seemed) in the Act of 5 November. It collapsed, however, after the oath crisis. Dmowski's idea collapsed as the Russia proved to be a country with little hope of liberating Poland, though a significant armed forces were organized in Russia.
Situation changed after kaiser direly needed soldiers to finish the war and decided to 'restart' the Kingdom of Poland properly and freed Piłsudski. This turned as a very good (in short term) and probably quite bad (in the long term) idea. In short term it managed to organize proper Polish Army, from both local recruits and former polish armies fighting besides Russian Republic prior to the explosion of Russian Civil War.
The Kingdom existed in a sort of a political vacuum, as nobody knew what exactly was going to happen to it now that it was no longer required. It was allowed to participate in Veimar Congress, but many things indicated that it was going to become a satellite state of the German Empire, even if with quite wide autonomy. This caused a lot of dislike towards already disliked German Empire.
Situation changed following the Ludendorff's Coup. It was a blessing to Poland - Piłsudski acted fast and decisive. Polish forces helped subjugate freikorpses and spartakists in both Greater Poland and Silesia - and then refused to leave. Of course, not openly, but Germany lacked firepower to pacify them. In Greater Poland local polish militias and 'temporary' administration quite quickly led to straight annexation - and Germany once again could do nothing. In Silesia a compromise was achieved, as it was the only major industrial region left, and taking it over from Germany could have grave consequences.
A compromise that is temporary. If Greater German Republic will be decisively defeated, Poland might suddenly remember about local polish population and simply annex this region (either directly or as an autonomy).
Soon after that, a draft of a future constitution was made (the so called November Constitution), with all German influences carefully eradicated. Less than a year - 12/09/1923 - later the so called Ober-Ost (officially German-held lands between Poland and the frontline, in fact under control of Poland since it took over the eastern front) was mostly annexed as well, with Germany managing to hold on only to Lithuania (but mostly because Poland didn't tried that... yet). The region was reorganized into two Grand Dukedoms under polish control.
But not everything is nice and pretty in the Kingdom. Piłsudski faces a lot of internal opposition. The Kingdom itself is almost a dual state, with Roman Dmowski (leader of National Democracy) almost rivalling him in influence, especially in the western - most developed - parts of the country. There is also a powerful socialist movement that doesn't sit right with the word 'Kingdom'.

Demography and Population

Heavily divided. Poles, Jews, Germans, Belarussians, Russians, Ukrainians, Cossacks, Tatars, Lithuanians, Crimean Karaites... It's hard to try to find two groups that lack some sort of painful or just problematic disputes. Poles are small majority, but it varies between regions. There are some where Poles are a minority. This isn't the only division. All main branches of Christianity coexist together with judaism and even (regionally) Islam, though their co-existence is much easier than national one.
Another division is of political nature. Strongest and best organized political party is right-wing Narodowa Demokracja (ND, National Democracy) under Roman Dmowski, that doesn't precisely like Józef Piłsudski. It also doesn't like other nationalities, though it's far from suggesting an organized violence. It's equivalent in the left is slightly weaker Polska Partia Socjalistyczna (PPS, Polish Socialist Party) that harbors exactly opposite views and supports Piłsudski (a regent of a de facto monarchy, for an added irony).
With political center (be it heavily fragmented Polskie Stronnictwo Ludowe (PSL, Polish Peasant Party) or smaller centre-right parties) weak and fragmented, none of the two sides is strong enough to form a coalition government. PSL drifts towards PPS, and the centre-right (mostly Christian Democrats and monarchist conservatives) drifts towards Narodowa Demokracja. Current national unity government holds together mostly because of the deadly threat. With pretty much every major party having at least a single major military group that is under their heavy influence, a civil war is a possible future threat.

Important Characters

Regency Council
Józef Piłsudski
Regent of the Kingdom of Poland, and the commander-in-chief of its army. A man of many ambitions, devoted completely to ensuring that the independence of the kingdom - that it managed to regain merely few years ago - will last for long. Former chief member of the PPS, left the tram of socialism at the Independence stop.
Roman Dmowski
A leader of the National Democracy, most powerful and best organized political part of current Poland. Nationalistic demagogue for some, inspired ideologist, political philosopher and patriot for others. Second most influential person in the Council after regent himself... whom he personally - and mutually - dislike.
Ignacy Jan Paderewski
A world famous pianist and composer... and great polish patriot. With extensive contacts in the Entente and United States of America. Co-opted to the Council for an international influence and closer contacts with United States.
Wicenty Witos
A son of a peasant family that grew into a tribune of all polish peasant. Leader of PSL, the only large political center party in Poland. Current prime minister of Poland and a person widely respected even by his political enemies, serving as a voice of moderation.
Wojciech Korfanty
A central point of polish influence in the Silesian region, and a man responsible for the strength of local pro-polish sentiments. Connected to polish Christian Democracy.
Military Commanders
Józef Haller
A general and a commander of Blue Army, an army trained from polish war prisoners to fight beside the army of the French Republic. Evacuated to Poland during the armistice accompanying the Veimar Congress. Nationalist and a supporter of National Democracy, with his soldiers a bit more varied in that regard.
Józef Dowbor-Muśnicki
A general commanding the so called Greater Poland Army, composed mostly of the inhabitants of the Greater Poland region seized by Poland following the Ludendorff's Coup. A staunch supporter of de-politicized army, but commanding over an army recruited from the bastion of the National Democracy.
Tadeusz Rozwadowski
Genius strategist and tactician, responsible for new doctrine of artillery usage (that helped break the first stalemate on the Western Front) and new type of artillery round of vastly improved quality. With Piłsudski mostly focused on politics and greater picture, he serves as a commander-in-chief for a commander-in-chief.
Others
Franciszek Rychnowski
An eccentric inventor, engineer, physic and photographer. Shunned before the war for dabbling in pseudo-science... but made a come-back when after the world changed he returned with a new type of thaumaturgy that by many is seen as one of the greatest trump cards of the Kingdom.