I can answer a part of this question, about why the Prussians had no great difficulty holding the Swedes off.

In theory, the system that had created the excellent or even superb Carolean army, indelningsverket or the alotment system was still in effect in Sweden. This meant that groups of self-owning peasants signed a contract with the crown, being absolved of tax (or rather, land rent) and being free from any conscription of themselves or their families if they provided a soldier, his equipment and a croft for him to live on as he served as a soldier. The officers got full farms on crown land and were required to live close to their soldiers and make sure the peasants delivered according to the contract and that the soldier lived a healthy life and was able-bodied and sound of mind. Since many officers were noblemen, this gave the soldiers "a friend in high places" and improved their lot in life. Combined with the ability to "see the world", wear fancy uniforms and getting a croft made the position decently popular before the Great Northern War, and the peasants rarely had difficulties in finding willing recruits.

However, after the death of Karl XII at Halden 1718, the whole system descended into a deep bog of corruption. Nominally, the officers were not allowed to buy or sell their farms, but there was an exception where they were allowed to charge their replacement for any improvements they had made during their tenure. In practice, this meant that "buying a comission" became common among the officers, and only having influence (ie being a nobleman and having the right contacts) and money became the requirements to become an officer. Even worse, noblemen started buying officer's positions and the farm that came with it without ever taking up the position, instead letting the land to local peasants and taking the income and never serving as an officer. There were many cases of officers having multiple comissions and farms and never serving any of them, only taking the pay and the income from the farms.

Of course, the lack of oversight meant that the peasants started to shirk their duties as well. Uniforms were not replaced as they wore out, muskets not repaired or replaced when broken, swords were allowed to rust and so on. It was not uncommon for peasants to spend some money to bribe the officers to note that equipment had been provided and then blame the soldier if any equipment was missing during a muster. The soldier no longer having "friends in high places" and the losses both during the Great Northern War and the Hat's Russian War 1741-43 made the position far less popular as well, and the peasants started having a hard time finding able-bodied and hale and hearthy men to fill the positions. In some cases men remained on the lists far beyond when they should have aged out or had become mentally or physically incapable of being soldiers, or even infirm. In other cases, peasants would list people they would want to get rid of - such as the village loon, a traveller or a farmhand that had suffered an acccident and become unable to work as well as he had.

The soldiers were supposed to meet by company 6-12 times per year to practice drill, live firing, manouvering and charging in formation. Once a year the regiment met for 2-3 weeks for larger exercises, and every 3 years, several regiments met for musters and large-scale mock battles. A soldier should spend somewehere between 2-3 months a year in training. However, with officers often absent or corrupt, there was a tendency for the peasants or even the officer to use the soldiers for manual labour during the time that was intended for drill and training.

Sweden entered the war reluctantly and without proper preparations. Austria claimed Sweden needed to join the war or forfeit its role as guarantor of the Peace of Westphalia, which would be a terrible blow to Swedish prestige. At the same time, France continued its policy to bribe the members of the Swedish parliament, and especially the prominent members of the ruling party, the Hat Party and by bribery forced the Swedish governemt to go to war. Sweden scrambled a force that was hardly trained at all, severely lacked in weapons, uniforms, ammunition, food and other supplies, with officers that had no wish nor intention to fight a war and many soldiers being infirm or incapable in different ways. Since Sweden went to war quickly without preparations, it was already at war when negotiations with France for subsidies started, at which the French gave far less than initially promised, since Sweden was already committed. Supplies, reinforcements and ammunition arrived in too small amounts if at all to the army in Prussia, and usually so delayed that the campaign season was over by the time they arrived.

Despite some innovation, such as introducing Jäger light infantry equipped with short rifled muskets, adapting Hungarian style Hussars and the newly created archipelago navy's victory over (and total annihilation of) the nascent Prussian navy at Frisches Haff 1759, the Swedish effort was really, really bad due to the army being a pale shadow of its former self, due to massive corruption at all levels.

The greatest Swedish contribution to the war would probably be a prisoner of war. A young nobleman from Mecklemburg had enlisted in the Swedish Hussar Regiment being set up in Pommerania and would be taken prisoner in a skirmish 1760. The Prussian Hussars he fought were impressed by his willingness to fight and quickly enrolled him in their own regiment, from which he made a bumpy career that would eventually end him as Prussia's most decorated soldier ever and a legendary status and eventually defeating Napoleon at Waterloo. By then he was known as 'alte vorwärts' ('old forwards') and Field Marshal von Blücher.