I realize that with the ongoing rythm, and as I cannot answer all questions with entries, I will now respond to your questions directly instead of managing suspense, except for the main points.
Did Vittorio Emanuele abdicate?
Vittorio Emanuele IV had been, before his accession, an embarassment to the throne, clearly aligning himself with the Alt-Fascist Party and military governments, with several financial scandals embarassing him. From his accession, he conducted shady deals with the Mafia and doubtful businessman ; a sex and corruption scandal drew the final line and royal immunity was removed in 2004 ; condemned to a prison sentence and losing his appeal, the King finally abdicated on New Year's Eve in 2007, and has since escaped justice, residing in Switzerland.
I see more monarchies than OTL, I like.
This Wikibox is one of my masterpieces. I also notice that Tomislav III of Croatia managed to beat this year Louis XIV's record.
I notice some countries have much higher populations than OTL (China, Germany at 2X OTL even) while some have much lower (Japan) and others roughly the same (Italy, France, UK). I’m interested to see how this came about.
To make it simple : China was spared from the monstruosities of Maoism, but it has never implemented the single-child policy and this 2 billion population draws significant stress upon economy, drawing large unemployment and tremendous inequalities. China has incorporated emigration into its foreign policy (to make it quick : if you need cheap workforce, we send you people. But if you don't comply with our tariffs and interests, we send you TOO MANY PEOPLE.) and Chinese migration is among the highest in the world. The Yellow Peril remains vivid in Europe, replacing the OTL Arab or African migrations in the minds of racists.
Germany was spared from Hitler and retains among the largest Jewish populations in the world, second only to the United States. The country also benefitted from migration, drawing from its former African colonies and Central Europe. Russia was also spared from Communism and has a positive net migration rate, as does Italy, the United Kingdom or the United States (that has a larger population thanks to China but also troubles in Mexico).
Japan conducted a settler policy that, along with its fertility rates going down, has conducted to deplete the population.
France's case is more particular : the country has had its shares of violent dictatorships and paid a heavy prize to alt-World Wars, but this population has much more to do with the 15-million Algerians living in French Algeria...
Wittlesbach as King of Scotland? Did they bring the Jacobite claim up again?
When Scotland became independent, the new government wanted a monarchy and they turned to the Jacobite line of succession in a show of chauvinism. As such, they drew to the Wittelsbachs : as the current King of Bavaria is childless, Robert IV of Scotland was born Prince Robertas of Lithuania, second son to the King of Lithuania, himself a Wittelsbach.
I assume considering they're a separate party from the Conservatives and the Progressives that the Republicans are a libertarian party ITTL.
The Republicans became from time to time a moderate right-wing party, retaining some seats in the Midwest and New England. It became more and more Libertarian these days : the 2020 Republican candidate is former Governor of Michigan Mike Cox.
Feel free if you've got other questions and want a particular set of Wikiboxes !