1)I think we are going a bit off topic with Ottomans there. The state itself could have modernized but it is near impossible keep the power vested in the Osmanoglu dynasty. They are bound to become ceremonial figureheads with time. I think this modernised *Ottoman Empire* wouldn't hold vast swathes of territory but most likely concentrate on Anatolia, Syria, Palestine and the Sunni parts of northern Iraq. Not sure how much land could they have in the Balkans, as I am not knowledgeable enough about the area. Thrace, Thessalonika, Albania and Bulgaria( dominated by the Turkish population) seem possible. The combined population would be ~150 million. If per capita GDP rises to half of Germany's you would have a middle eastern power with 4 trillion dollar economy.
2) Any suggestions for POD dates?
(preferably single POD date scenarios) I posted a possible POD and scenarios in post #18
Actually, to have the Ottomans evolve into a modern nation-state you would need a more constitutional rule (i.e. abolishment of absolutism) and some sort of economic integration of all its territories.
Reforms would also be needed to create more modern institutions, financial, governmental, or otherwise. Unlike, say, the Austrian Empire/ HRE, a modern Ottoman nation-state would go for the opposite of Metternich's policies and incur reforms promoting fiscal liberalization. Though the problem on the economic front is that the Mediterranean economic region was basically stagnant, and it will be hard for the Ottoman state economically.
E: OK, there are several issues when it comes to the Ottomans building effective state capacity and thus establishing a modern nation-state. The Ottomans need to get rid of their tax system and go for more fiscal centralization. Think of Austria-Hungary imposing the Cisleithanian system taxation on Hungary after the revolutions of 1848.
The Ottoman bureaucracy needs to be expanded with administrative reforms, with all the fiscal and governmental apparatus centered on Constantinople. And there needs to be a development of a stable regime based on constitutionalism and parliamentarianism. In the rest of Europe, this sort of thing only came about after revolutions!
A strong state emerging from the above political reforms will be able to hold the Ottoman realm together. The peripheral states won't be able to secede easily, and the other great powers won't be able to undermine Ottoman authority by formenting nationalist dissent in the peripheries. This also would allow for the creation of an Ottoman cultural identity into which the elites of all the disparate ethnic groups can assimilate, in contrast to a national identity based on ethnicity which will only fuel secessionist ideologies.
The Ottoman identity spreading to the Balkans and Middle East will prevent other great powers from meddling, and prevent the populations of the non-core groups from identifying in solidarity with other great powers, e.g. the Slavs and Orthodox Christians to the Russian Empire. The ruling political elites of the Slavic territories, Greece, Arab territories, Maghreb etc. should identify part of the Ottoman core, influenced most by Constantinople than anywhere else.
If an area at the periphery is considered unimportant by the center, and isn't integrated as a result, that makes it easier for external powers to lead them away. The Ottoman state should prevent this at any cost, and focus on integrating all territories it can through sociopolitical means and through fiscal and governmental organization.
In Conclusion, the modernized Ottoman state wouldn't be a nation-state in the form of Germany or France at all. A strong Ottoman state would have long abandoned its original system of taxation in favour of one that's more effective, centralized, and uniformly imposed.
The old system of absolutism would have been transformed into a more limited structure based on parliamentarianism and constitutionalism. There wouldn't be a notion of a core Ottoman population of Muslim Turks, but rather a high-status Ottoman identity in which the political elites of all Ottoman regions would be folded into, perpetuating the imperial institutions that will prevent nationalist secession in the periphery. While nationalism in the periphery won't necessarily end, as ethnically homogeneous groups concentrated within a region will always end up creating their own institutions based on their cultural distinctions, targeting the sociopolitical elite will ensure the preservation and consolidation of Ottoman institutions, and ultimately lay the foundations for a strong, self-perpetuating, Ottoman state.