First things first, it was just the plain old Duchy of Warsaw not a Grand Duchy. It's a long standing misnomer that refuses to away (even in academic literature) - by population, Warsaw was bigger than any the states of the Confederation of the Rhine so even the Grand Duchy name would seem inadequate - but the Polish name was Księstwa Warszawskiego where Księstwa is usually translated as Duchy or Principality, in this case as Duchy - coins were inscribed FRID AUG REX SAX DUX VARSOV (Friedrich August, King of Saxony, Duke of Warsaw).

As for why a Saxon chosen, it's important to remember that Friedrich August (hereafter just Friedrich) wasn't just some random malleable German noble chosen by Napoleon. His grandfather and great-grandfather had been elected as kings of Poland during the 18th century (Augustus II "the Strong" and Augustus III). After the death of Augustus III, Friedrich's father Friedrich Christian reigned for less than 3 months before dying of smallpox in 1763. This had left insufficient time for a royal election to be organised in Poland; Augustus III had been attempting to set up his youngest son as an attractive candidate for the throne by making him Duke of Courland and Semigallia in late 1758, however the weak position of Saxony during the Seven Years War and pressure from the recently crowned Catherine II of Russia prompted the Duke to renounce his throne in late 1763. By the time the Royal election was organised in 1764, Friedrich was an unpopular candidate being only 12 years old the time. The other two candidates were the elderly Grand Crown Hetman Jan Klemens Branicki and Catherine's favoured candidate Stanisław August Poniatowski (her former lover). Poniatowski was duly elected and the regent of the Saxon Elector formally renounced Friedrich's claim on the Polish throne in 1765, following on from the Electorate being overrun by Prussia during the Seven Years War. This renunciation was part of the terms of the Russo-Prussian treaty of alliance signed in April 1764 that sought to strengthen control of the Commonwealth by those two states.

Friedrich next makes an appearance as part of the Constitution of 3 May 1791. Written at a time when Russia was occupied with wars against Sweden and the Ottomans and thus could not interfere with the Polish parliament while the constitution was drafted; amongst many other reforms to the Commonwealth government, the monarchy was changed from the traditional elective system to a hereditary monarchy where executive power was held by the king counter-balanced by a council of ministers (comprising the Primate of Poland and 5 ministers). The change to a hereditary succession meant that foreign interference in the Royal elections would be prevented - ironic given King Stanisław's key role in the drafting constitution that he owed his position to Russian interference in the 1764 election. This was specifically outlined in Article VII of the constitution which stated:

"Disastrous experience of interregnums periodically overturning the government, the obligation to safeguard every inhabitant of the Polish land, the sealing forever of avenue to the influences of foreign powers, the memory of the former grandeur and happiness of our country under continuously reigning families, the need to turn foreigners away from ambition for the throne, and to turn powerful Poles toward the single-minded cultivation of national liberty, having indicated to our prudence that the throne of Poland be passed on by right of succession."

Should the ruling dynastic line fail then a new dynasty would be chosen via election. As Stanisław had no legitimate children (though he did have a nephew Józef via his brother, who would gain fame as a general during the Commonwealth's final days and as one of Napoleon's marshals), Friedrich was chosen as King; interestingly he doesn't seem to have been fully convinced to accept and his consent would be required before he would be crowned, a diplomatic mission had been sent to Dresden led by Adam Kazimierz Czartoyski to persuade him to accept. The crown would be passed onto his legitimate male descendants; in the absence of any sons, the husband of his daughter Maria Augusta Nepomucena (who was specifically named as an infanta in the consitution) would begin a new royal line - this seemed the likely outcome as Maria Augusta (born in 1782) was Friedrich's only surviving child by 1791, though another child was stillborn in 1797. Wikipedia says that Józef was considered as a potential husband for Maria Augusta without sources. The 1791 constitution did not long survive - a victim of internal opposition and the Polish-Russian war of 1792 which culminated in the Second Partition. Stanisław was forced to abdicate in 1795 at the time of the Third partition.

The Duchy of Warsaw was created as part of the Treaty of Tilsit in 1807, largely out of former Prussian territory taken during the partitions (Austrian Galicia would be added after 1809). Exile Poles had long served in Revolutionary France's armies and a local rising had driven the Prussians out during the recent War of the 4th Coalition following an appeal from Napoleon; this made the recreation of a Polish state a key part of the treaty negotiations. Tsar Alexander was amenable to the idea of a recreated Kingdom, influenced by his friend Adam Jerzy Czartoyski. During the negotiations both the French and Russians were pushing the other to reform the Kingdom - Napoloon initially suggesting the Tsar become King of Poland in exchange for Prussia ceding the rich province of Silesia; the Tsar rejected this and instead suggested Napoleon's youngest brother Jerome as a candidate for the Polish throne - Napoleon instead took Prussian territory on the left bank of the Rhine (amongst others) to form the Kingdom of Westphalia for Jerome. Friedrich was the natural compromise candidate. The new constitution was inspired by that of 1791, though transformed with ideas from the French revolutionary period and the Code Napoleon, with a key difference being that succession laws (Article 5 of the Constitution) would be based on the Saxon house laws rather than passing to any husband of Maria Augusta (she would never marry and her Uncle would take the throne after Friedrich's death). The powers vested in the Duke gave him near absolute powers (article 6), however he could transfer those powers to a Viceroy (article 7) or a Council of Ministers (article 8) - this council comprised the Justice, Interior, War, Treasury and Police ministers and a Secretary of State who resided in Dresden and acted as a liaison between the King and the Government. Given that the Government was almost entirely Polish and Friedrich largely left them to their own devices on internal matters, this was not a cause of great friction to the Poles - after 1810 the council of ministers could execute decisions without prior authorisation of the King. On the eve of the invasion of Russia in 1812, Friedrich delegated all powers to the Council.