This is very interesting, due to the fact that without the conquest of the Incas, the colony (country) may have to colonize the region of la Plata as well. Taking control of the Amazon Rivers and Rivers of the prata Basin. if it is two countries, we have two very strong Muslim powers. With one in the grancolombia region and one in the otl region brazil and argentina.
I was actually planning on splitting up the Muslim parts of South America into 4-5 different countries of varying strengths - mostly for gameplay purposes as these nations will start ahead of the Incas in terms of technology and so I'd want them to have to struggle with each other before being able to face the Incas in a theoretical conquest of South America.
However there's also some root to this in history, as in otl Islamic colonization of regions was very different from Christians, where it was mostly independently done by traders who would proselytize to the regions they traded with. Something that's important to understand here is that in this timeline, the Cordobans discover the Americas in the early 1400s thanks to a few merchants that blew off course and accidentally landed in Brazil, and when they do, they don't really see the Americas as "virgin lands" to be colonized and conquered at first, and for a little while mostly just engage in trading with the local natives, eventually making contact with the Mesoamerican and Incan civilizations. This is important because these traders bring with them the diseases that absolutely destroyed the Native Americans in our timeline and made them ripe for Spanish conquest - but by the time some muslim merchants get the bright idea to start building plantations to start producing selling cash crops like sugar and coffee, these diseases have already burned their way through the indigenous populations of the Americas, and actually American population levels are starting to rise above pre-discovery levels in certain areas thanks to the new methods and resources the Berber and Arabic merchants spread in crop production. In most cases this simply means the merchants marry into the local ruling class and use the rest of the populace as a workforce for plantations - though in some more fertile areas like the La Plata where the Charrua and Guarani populations were exploding, they were actually conquered by a Cordoban conquistador who had some bright ideas. In any way they took over, the rulers of these areas still pledge fealty to the Caliph of Cordoba, it's just thanks to the distance and indirect way these regions were acquired that they essentially run themselves as independent nations.
It's also through the insane profits the Arabic and Berber merchants make by building plantations in the Americas that attracts the attention of the European Christians, and leads to the French, English, Scandinavian and Dutch settlement of North America and what's left of the Caribbean in the late 1600s.
Not Hadrada himself but his grandson, Magnus Barefoot - known in this time as Magnus the Great, who exploited the weakness of Harold Godwinson's heir to press his Grandfather's claim.
was there a religious break between cordoba and the western caliphate?
Yes actually, to the point the Cordobans, the Berber parts of North Africa, West Africa and the Americas actually follow a fictional sect called the Almumini, which believe that the Head of State of the Emirate of Cordoba is actually the true Caliph, rather than the Arabic Caliph the Sunnis believe in. I say "Arabic Caliphate" because truth be told though I haven't fleshed out the Middle East itself just yet as I really need to study it some more to figure out who I want to control it. I do want a decently sized power to do so, but the thing is I'm planning on Byzantium surviving (though only really as a backwater rump state that's barely kept alive thanks to the wealth of Constantinople as a city and the help of the Hungarians and PLC that is essentially only Greece and Eastern Thrace). That essentially knocks out ever having the Turks coalesce around a single power - and I don't really want to do the Ottomans anyways as they've been done to death. The Mamluks were already in decline by the time of the Ottomans anyways, so there's no way they'd survive to the 19th century. I'm considering having the Safavids be it, but I'm also considering just coming up with some other nomadic turkic/caucausian people who conquer the Middle East instead as that's been the trend of the Middle East for much of recorded history. Which of them would be an interesting candidate is what I need to look into.
In a manner of speaking yes, but also no. The PLC will be kind of analogous to the Russian Empire here, controlling Poland, the Baltic States, Ukraine, Belarus, and Russia (Haven't decided what I'm going to do with Siberia just yet, I think I'm going to have the Chinese colonize it and have it as an expansion route for both an independent Russia or a Japan but I don't have Asia fleshed out that much in general), but all other peoples than the Polish and Lithuanians are treated as second class citizens who have no say in the government and are treated mostly as serfs and are exploited by the ruling Polish and Lithuanian nobility. This is going to run face first into liberalism, industrialization and most importantly nationalism of the 19th century, where the PLC is either going to have to find an ideological reason like Socialism to survive and maintain their union, or they are going to break apart at the seams and have every ethnicity under their banner demanding their own nation and they will have no choice but to let them as the Poles/Lithuanians simply do not have the manpower like the Russians did in OTL to keep their realm together by force. That being said even if that does happen, the PLC itself with just Poland and Lithuania will still be a force to be reckoned with as Poland and Lithuania as regions themselves are wealthy in this timeline and have undergone much industrialization - so no matter what the player will have options with what they want to do with the country.